Quant Mock Interview 2: Time Series Modeling

[00:00:01]Hi everyone uh this is Mayol Mat and welcome back to my YouTube channel. So we are trying to simulate a mock interviews for quant and risk uh interviews in general. So the topic for today is time series modeling. Now time series in general it's very important if in case you are working for any hedge fund because they use time series left right center. Similarly if you are working at a bank we use time series for capital management. So again uh specifically for PP&R modeling. So again time series is very important. So in general if you're planning for banking risk management or hedge funds in general time series as a topic is very important. So that's why we are trying to practice this topic. So let's start.

[00:00:44]I'll ask the question and all of you whichever you know whosoever feel confident just tell the answer. Okay. So let's start. What is time series modeling and what are different components of time series?

[00:00:58]Who would go?

[00:01:02]Try. Let's try. Let's try.

[00:01:04]>> Shall I go for it?

[00:01:06]>> Yeah. Yeah. Jenga, please go for it. And make sure to turn on the camera so that we understand.

[00:01:11]>> Uh okay. Uh is it necessary like Okay.

[00:01:15]It's just 7:00 a.m. So I'm not really ready. Okay. I'll go for the answer.

[00:01:21]Yeah. Uh the basically time series modeling is uh uh collecting a data over a period of time and uh using it for modeling and uh projecting purpose uh and it might have a component. For example, we can have a uh data of a share price uh which is collected over a uh month on a daily closing price basis. So it has a components like variation, mean value and autocorrelation and uh we can use it for modeling and projection purpose for our future use.

[00:02:00]>> Okay. Certain issue with the definition.

[00:02:03]Who wants to go next? I'll tell you what the issue is. When you say components, the components that you mentioned are not right. Autoations are like statistical test. Okay. So I I'll let Konarch say. Yeah.

[00:02:16]So if we uh tensis modeling is taking observation and finding pattern and seeing which of variable are dependent on [clears throat] which are previous values and how much dependence are there on the values. So uh in the components uh uh the components that we use is uh there's a baseline uh value that we take in our equation and the model then >> what is called >> like uh the baseline variance or like uh omega KN in the equation uh which we call >> okay >> and [clears throat] then we take how uh so we are taking example of volatility we are trying to predict or how much volatility dependent on the previous factors of previous shocks. So we try to compare it with the previous news factor. How much uh dependence was there on the previous news factor. Then we try to compare how much residual was there from the previous uh variance of previous volatility and then uh a baseline volatility in the equation. So these are multiple components that are there in the equation.

[00:03:32]uh it's kind of different than the other models because uh uh in the other models most of the time we see data clustered together but in the times modeling we try to find a pattern in a longer duration.

[00:03:49]So uh uh and see the observations sequently like how are they dependent on the previous observations. Okay, it's a very simple answer. You have made it complicated. Parish, let's go with Parish.

[00:04:02]>> Okay, so time series model is basically collecting data successes successively at equivalent intervals of time. So it can be done weekly, daily, annually, monthly. So the most important thing in time series data is the chronology. We cannot shuffle the data in any order. It should have a proper time stamp as occurring naturally. And the various components of time series is uh namely trend, seasonality, cyclic pattern and the random fluctuations. So trend is actually the long-term uh upward or downward movement of the data. Cyclic pattern is basically the long-term oscillation of a data which is of unknown period. Seasonality is a repetitive pattern observed in the time series data over a known period of time and random factuations are basically like those patterns which cannot be uh predicted or which cannot be we cannot have any distri I mean we cannot have any pattern for them perfect I believe it's a beautiful answer very simple what is time series modeling we basically we are trying to model a variable Right? What variable is it? It can be any variable. Inflation, interest rates, it can be anything. Unemployment rate. Right? And what how do we do it?

[00:05:20]First, first thing is to collect the data. Making sure we have see time series analyst is nothing but analyzing any variable which has time associated with it or modeling. Time series is nothing but any modeling any variable which has time associated with it. As he said, we cannot shuffle the data. And what are four components? trend, seasonality, cyclicality and random fluctuation.

[00:05:43]That's it.

[00:05:46]Cool. Great answer. I feel very nice answer. Okay. Second question specifically to Konach. Um, what do you mean by stationaryity of a time series?

[00:06:02]Stationality of a time series.

[00:06:07]Equally stationary uh mean zero median zero or coariance constant uh systemarity of the data I'm not able to like grasp the definition for the stationerity like I I'm able to explain like what is weak stationary or like uh >> uh how to find the >> how to find the strict strict stationary >> testing but like uh stationaryity of the data like dependence uh like the definition should be around the dependence like uh we try to compare how much dependence is there on the previous variable like it shouldn't be time dependent it should not be time dependent >> correct >> you give me the answer see I I just want the complete answer I don't want bits and pieces yeah yes yeah >> so like uh stationary is a like a type of time series data a time series time series in which our mean is constant our variance is constant and our auto autocorrelation is also constant like it's it is not like uh >> that's right I mean three things that we require for stationity of any variable first thing whenever we collect the data right we check for stationity whether the variable is stationary or not what do we check if the mean is constant if the variance is constant if the autocorrelation is constant If it's if any of these conditions are violated, what happens? That means that the variable is non-stationary.

[00:07:44]>> So now the next question is how do you conver what? Okay, two questions. Okay, let's go one by one. How do you convert a non-stationary data into stationary data?

[00:07:54]>> Can I go back?

[00:07:56]>> Uh clear.

[00:07:56]>> Okay, Ian, let's let's go with Ishan.

[00:07:58]Yeah.

[00:08:00]>> Oh. uh to convert uh a non-stationary data to a stationary data we take the returns uh uh either the log return or the simple return uh based upon the model usually in time series we take the log returns because of the uh multiplicative part. So yeah and uh there are two tests for stationerity uh one is uh kpss and the other one is uh dicular test. Okay. Now when the question I asked is your answer is correct that you said you you can either take log return simple returns and that can give you basic that can convert a non-stationary to stationary but from a interviewer's perspective I'm not satisfied with your answer.

[00:08:49]I want if let's say if I ask you five different ways how you convert a non-stationary data to a stationary data. How many of you can say >> I can?

[00:09:00]>> Okay, let's let's go. No, if you are confident then race.

[00:09:07]>> So first is differencing.

[00:09:09]>> Yeah.

[00:09:09]>> Second is >> so when you when he par is differencing there are two ways. First order differencing and second order differencing. In both the ways you can convert non-stationary to stationary.

[00:09:18]Yeah.

[00:09:20]>> Then seasonal adjustments can be done.

[00:09:22]We can remove the seasonal patterns.

[00:09:24]Then we can go for transformation.

[00:09:26]Transformation is just like Ishan mentioned. We can use mathematical functions. It can be a log function. It can be a square root. It can be any other function. Uh then we can also go for drending of the data. We can remove the trends.

[00:09:41]>> Yeah, pretty much. Yeah, pretty much he answered.

[00:09:44]>> But like so uh can we use also co-integration in this?

[00:09:51]>> Why?

[00:09:54]Because like most of the time we use co-integration in some of the models like we take non-stationary data which we see like uh is uh doesn't have mean constant or variance constant like uh let's say price of one one product and price of another product. They both are non-stationary at the moment. But if we try to find the beta into them and uh co-integrate them. So the spread that we get would be stationary at this moment and we will be able to trade that.

[00:10:28]>> I guess co-inttegration I believe it's more like if you have let's say two stocks stock A and stock B both are non-station then you apply these concepts. My question is very simple.

[00:10:40]How do you convert a non-stationary data to a stationary one? That's what parish answered. I what I want is see all these techniques you'll use in real time also.

[00:10:51]Okay. It's not something uh you will not use. For example, if you want to let's say uh more if you want to try to forecast what is the mortgage balance next month over month or quarter over quarter, you would not just take the mortgage balances for last 10 years and try to forecast it. First thing you do is differencing.

[00:11:13]So first order differencing, second order differencing, log transformation, uh square root transformation, cubic root transformation. So when do we use square root or cubic root? When the numbers are too big. That's why sometimes stabilize the variance.

[00:11:26]>> Yeah. Sometimes log might not work log transformation. So that's why you take cubic root transformation.

[00:11:33]>> Okay. Let's say the mortgage balances if the balances are in like million billion dollars. Sometimes you take all this cubic transformation. Some sometimes you do drending uh you remove the seasonality because you're seeing only in let's say June, July, August you see certain pattern going up and then otherwise it's flat. So you just take out that remove that pattern, right?

[00:11:54]Okay. Now what is augmented dqiful test and what is how is it different from the kpss test?

[00:12:04]Uh so the augmented dicker test uh the null hypothesis for that is uh it's uh checks for whether there is a unit route means uh the time series is non-stationary and for the kps test uh the null hypothesis is the it assumes that the time series is stationary.

[00:12:28]>> No no I did not get you can can you say that again? So one is unit root and the other one is >> uh it checks the time series is stationary or not which is the kps >> time stationary.

[00:12:40]>> So how >> the time series is stationary? Yeah the kps uh null hypothesis is uh the time series is stationary and for the uh augmented digular test it is uh the null hypothesis uh text that uh the there is a unit route or not. Okay. But then how are they different? What both are both are you know both are test for testing the stationity. So how are they both different?

[00:13:09]>> KPSS checks checks for trend stationary.

[00:13:12]>> Stationary. Yeah.

[00:13:14]>> And >> test for stationary.

[00:13:18]>> Yeah. Difference stationary. You can say >> difference. That's right. Okay. Perfect.

[00:13:23]>> In one way like uh augmented test is ADF.

[00:13:28]>> ADF. ADF test. So like u in ADF test like uh we unit uh root test and like in KPSS we do uh stationerity test and uh like for ADF like the data is non-stationary for KPS like the data is stationary and >> no no wait both of them are used for testing stationary >> only difference is ADF used to test test different stationary If you know when you perform differencing and then when you perform this whereas in KPSS it's specifically for trend stationary.

[00:14:08]>> Okay. What will happen if one says let's say if ADF says it's stationary but KPSS says it's non-stationary. What would you do?

[00:14:19]>> Uh check the P values.

[00:14:22]>> Yeah. What the P >> P value is less than like um >> yeah with the P value. So if it reject H0 like >> listen to me with the P values only you you tell the conclusion I'm saying the conclusion only that let's say one test ADF says it is stationary whereas KPSS says it is non-stationary what would you do because >> and this is a practical problem because I remember a model validation team asked me to do both the tests and report both the test and there will be times when one is stationary and other is not what would you do?

[00:15:00]>> So if KPSS says it is not stationary, it means it is not trend stationary. The time series is not trend stationary. So we have to remove the trend first.

[00:15:10]>> That's that's right. Simple.

[00:15:16]Perfect. So now what is AR model?

[00:15:22]AR is auto reggressive model which basically regresses the present value of the time series with its own past values. So a simple AR1 model would be of the form of let's say the current value is YT then YT would be equal to a constant plus beta * YT minus 1 plus epsilon T where epsilon t would be the residual and beta is the parameter which is to be estimated.

[00:15:46]>> Okay. How would you estimate the beta parameter?

[00:15:52]uh using the stats model in Python package we can fit the data >> but then what's the underlying >> the maximum likelihood estimation >> by using the >> that's the way of calibrating but the underlying >> so we can use the I mean we can use the P uh PSF graph PSF plot to estimate the order of the air model >> no my question is how >> he's asking beta >> coefficient how would you determine the coefficient >> like [clears throat] from one spread to another It's a flow.

[00:16:22]>> Can we average? Can we average out the difference like various variance which was been experienced in previous uh training?

[00:16:29]>> Regressing regressing the data onto one another and finding the beta over it like the same example uh like I talked about the spread can't we use that?

[00:16:39]>> Yes that's what that's what it's a it's a simple linear >> linear regression.

[00:16:44]>> Okay.

[00:16:45]>> Right. It says that we are regressing our current variable with the past values. That's it. It's a regression in the end. Okay. Time series is nothing but a linear regression. Okay. Okay.

[00:16:55]Next question. So what is a MA model?

[00:16:59]And I want any any other person to answer other than parish MA model.

[00:17:07]So the MA model is uh the moving average model uh where uh it assumes that uh the current value is um based upon the past residual shocks uh uh if the current value is yt. So the ma1 model will would be yt is equals to some constant plus beta * epsylon t minus1 plus epsylon t where epsylon t is the uh current uh residual and epsylon t minus one is the past residual.

[00:17:40]>> Perfect. Very nice. How would you determine the lags in the ar and ma model? So the lags in the MA model is determined by the uh PACF uh uh ACF graph and uh uh for the AR model it is determined by the PACF graph.

[00:17:59]>> PCF plot.

[00:18:01]>> Yeah. PCF plot. Okay. So what is ACF and PACF plot? Can you tell more about it?

[00:18:08]>> Yeah. Uh the ACF stands for the autocorrelation function. So it uh it is like the Pearson correlation coefficient where uh we just check that uh means uh it it accounts for the indirect effect also means uh if uh it doesn't capture the individual effect of of the shock it uh captures all the uh indirect effect also but in terms of PACF we get the uh means what a particular time uh means value is affecting our time series. So, uh this is a basic difference like we get the beta terms in P uh PSF like how much that parameter is affecting our value.

[00:18:52]>> Okay. Anyone else who wants to try what is ACF and PSF?

[00:18:56]>> Uh yeah, I I would try. Uh so in ACF we take uh the uh uh use of past complete duration. However, in PSF we take the immediate previous one uh on the graph.

[00:19:10]Uh how would you differentiate that Ajinka?

[00:19:15]>> Basically on graph give me an example.

[00:19:18]>> Yeah give me in yeah yeah in ACF we might get the you know um high high values on multiple occasions. Uh however in PSF we we can get the peak on a immediate previous uh occasion only.

[00:19:34]>> Are you sure on that? What if it's a what if if it's a seasonal pattern >> let's say every six months you get the high the peak >> in in that case uh but in PACF we uh we won't take that uh longer data we take the uh previous uh recent data >> okay when you say PACF you are referring to AR model right AR model you take lags up till 12 let's say if you have monthly data right you 12 lakhs which means last one year you check which you know what's the correlation between each month >> sometimes only in the six month you know let's say it's something like that let's say you have a shop of mortgages let's say you are a mortgage bank you see most of the mortgage being or originated in the month of summers you know this June July may June July August so that's why you'll see all these four months the sales being pretty high or In general the you know people apply for more mortgages loans but other months they do not apply much. How do I know because I've worked on the mortgage portfolio.

[00:20:47]So so anyone else who wants to answer this?

[00:20:50]>> Uh yeah >> ACF.

[00:20:52]>> Yeah go back. Yeah.

[00:20:54]uh ACF is a correlation between uh the current value of the variable with the previous value of the variable taking the intermediate lags considering the intermediate lags. PCF uh PACF is the partial autocorrelation where we try to find the correlation between the current variable and the previous variable but removing the shorter duration uh lags from that >> that's the right that's the thing I was looking for removing removing the in between in between lags effect that was the exact thing I was looking for okay all right um ACF okay can you tell me okay I have a scenario based question okay let's say we are trying to model a mortgage balances okay and you saw that with AR1 let's say you took AR1 as your model okay and we are just referring to AR1 we will not consider MA we are just referring to AR1 you have a mortgage portfolio let's say um in you saw something weird happening in COVID period you know your mortgage is going some weird activity in your mortgage balances. How would you account for that? Uh first and let's say if I want to consider some other macroeconomic variables, how would you do the whole modeling?

[00:22:21]Let's go one by one. How would you accommodate for let's say for this weird behavior in the COVID era of your portfolio?

[00:22:31]>> Just raise hand. I'll ask just raise hand. Who wants to go first?

[00:22:37]>> I know the second answer. First one I'm not sure about it.

[00:22:40]>> Okay. Anyone answer?

[00:22:43]>> Yeah, >> I think we can use the dummy variables in that case.

[00:22:48]>> Perfect.

[00:22:50]This is for everyone to understand. If in case let's say you are trying to model some portfolio or anything and you see certain uh activity which is little off than the regular activities you just take a dummy variable to account for that. So what you do is you during so when you create your whole data set right you take let's say a dummy variable called covid during that weird activity period you just put 11 one one for those specific days or months and for all the others you'll just take as zero so what will happen when you regress eventually it's a linear regression right so it will automatically because in that period that covid term the covid variable term is one during that weird behavior appear. So automatically the regression will capture it.

[00:23:41]So now let's say we know that now COVID is not there. So what will you do for this COVID variable? When you have to focus, you'll just put as zero. In the forecasting period, you keep the COVID variable as zero.

[00:23:58]Clear? Please tell me. If it's not clear, tell me 100 times. But I want this. This is situational based question asked in multiple interviews because during the co time lot of variables got you know little bit off track that's why we take a demi variable to capture this weird weird behavior. So it's something like smokeote.

[00:24:27]>> Sorry, can you say that?

[00:24:29]>> Something like smokeote. Smote you. It's more like you are just averaging out, right? I believe >> what is?

[00:24:41]So uh smart is like a like we do a synthetic uh sampling like it's called a synthetic uh monitoring over sampling technique. So >> why why do we need a sampling here?

[00:24:59]Uh so my point of view of understanding was like I was asking was something like sport is like we do uh uh similar kind of uh event we add synthetically like u like what we do in card um credit risk uh I'm not able to match it properly. Okay, no problem. No problem.

[00:25:28]>> I know this uh I know this uh smart thing like which Hush is saying. So I have also worked on the created one. So smart in this mod like if we have a two categories thing. So if if the data is skewed to only one category we put the we take the dummy variable create the dummy variable to another for the other category so that the uh we got the result like for the both the ones if not the result should not be skewed to one one.

[00:25:51]>> Oh it's the data credit right? Yeah. Yeah. We sampling data.

[00:25:57]>> But I my professor said one thing like uh if you use deep learning model like the ML techniques in the time series uh many times what happens is the data uh overfits easily because of having too many variables or like uh like because of the pitfalls of ML. So that's why we go for time series modeling over there.

[00:26:22]So does smart like uh >> help in that like problem?

[00:26:27]>> No no no no like smart generally works for like the cate category things like if we have a data skewed to only one category and the result should not be focused on that category. If we run a regression so if we have a multiple like lot of variable me like associated with the one category. So if we run the regression it will give that answer only. It's a false or false.

[00:26:47]>> Yeah. Basically, let's say in like a creditor risk let's say 98% people are healthy or good but that 2% people are >> default default. So what model will say that's 98% accuracy. So to focus more on that 2% and we use this mode or uh adding weights uh techniques and because of that uh it will the accuracy of model will decrease and like that. So >> okay positive.

[00:27:20]>> Yeah. Yeah. Okay. Let's but smooth is not used. Okay. What we Okay. So to answer that smooth is not used. What we use is we just create a demi variable, switch it on during the time it's behaving weird and just switch it off during the regular times and then when we do the forecasting we still switch it off until and unless we know that that specific event is again going to happen.

[00:27:42]Okay. Second question what I asked was let's say if you have variables how would you forecast?

[00:27:50]uh we can make a uh equation for that and try to go for the co-integration and uh uh form a VA model over here.

[00:28:02]>> There's no need there's no need of V. We can ar max model.

[00:28:08]>> Yeah.

[00:28:08]>> A rx it's called with endogenous exogenous or endogenous >> exogenous exogenous variable which means what?

[00:28:18]Let's say you are trying to model mortgage portfolio which is y. So what you'll do the equation will look something like this. YT is equal to some constant plus beta * YT minus 1 plus beta 2 * HPI plus beta 3 * unemployment rate simple it's a simple linear regression model >> sure >> it's called AR X >> so this X is you can have th different variables uh which you which can affect the housing market >> a max A R X A R X >> regression model it's it's a so you keep so how do you create a data set right you let's say YT YT minus one HPI unemployment rate right and then you're just regressing your X Y with X1 X2 X3 that's it >> multivariable regression >> yeah multivariable regression >> I think in time linear regression is used generally in the most of the case.

[00:29:24]>> Yes. Yes. It's a regress simple linear regression. Okay.

[00:29:28]>> Cool.

[00:29:29]>> Now what is ARAX and when can you and can you define the terms or the components of ARAX?

[00:29:38]>> So >> or let's say ARMA let's put it simple.

[00:29:41]Do you can you define what is ARMA model and what are the components? So uh ADMA stands for auto reggressive integrated moving average model. So uh if if we consider uh a basic uh integrated factor of one. So we are doing one p uh first order differencing and uh based on the orders of the ma uh a and ma model we form the equation means uh if it is uh on the first order differencing we are basically uh making the model as del yt is equals to some constant plus del yt beta * d ytus 1 plus uh uh beta 2 * epsylon tus 1 plus epsylon t.

[00:30:28]>> Okay, correct. So basically ARMA is nothing but it's a combination of AR, MA and I stands for differencing or you know integration basically. Uh so if you if let's say your data is not diff if you have not performed any stationerity or any kind of transformation then you can just put is1 which means first order differencing. when you put IS2 it means second order differencing and then again a R and MA are nothing but your P and Q are nothing but AR and MA component. I have a very good question on this. Let's say your insample data when you use this area model it worked pretty well for your insample data but when you performed out of sampling you know forecasting it performed very poorly.

[00:31:10]What can be some of the reasons?

[00:31:13]So your insample data is pretty good but out of sample is pretty bad.

[00:31:19]this clarity maybe overfitting >> because we already did differencing on a stationary time series data so it led to overfitting.

[00:31:30]>> Yeah, the answer is it's a overfitting that the it it basically the model overfitted and that's why when you take the out of sample data and it's not performing it's a proper uh classical example of overfitting. So what do you do when you have overfitting? What what steps do you take?

[00:31:52]>> Uh we will reduce >> sorry >> reduce the variable.

[00:32:00]>> Very nice. Sham has said so when it's overfitting means what? It's learning too much from the standards. It's learning too much. So what you do? You make the model simpler by removing the variables. Right? So that is one way.

[00:32:14]What other ways or how can you deal with the >> reduce the d factor that we have in the stationerity over there?

[00:32:22]>> What is the d factor means? What >> like uh uh how I learned the equation is like uh the uh alpha factor into 1 minus uh lag factor raised to power d yt * equal to the ma model. So this d factor is kind of like helps in the stationerity thing. So if the model is fitting well on the insample data, we can reduce the that D factor which helps to like uh uh handle the non-starity so that it fits on the out of sample data.

[00:32:57]>> Okay, I have not really worked on the D factor to be honest connect. I'm not the best person to judge if it's right or wrong because most of the times what we generally do is uh either we increase uh either we uh we reduce the number of variables that is the best way or we go >> this reduces the number of variables.

[00:33:18]>> Yeah. Yeah. And and then or what we do is next is we can use some regular regularization techniques like lasso and ridge or elastic net. Okay.

[00:33:27]>> Which are perfectly suitable when you have like lot of variables.

[00:33:31]Okay. Okay. Perfect. So, a quick question that another situational based question is um um let's say just give me one second.

[00:33:42]Okay. You have you have uh you find two bank stocks. Okay. Two bank stocks that have a correlation of 0.95 over the last 3 years. Can you immediately use it for pairs trading?

[00:33:58]>> No. uh because they may not uh uh like uh they may not be uh stationary and they not may they may not uh qualify the unit >> unit to you press test is more important correlation is a primarily can be seen for initial analysis however we need to do ADF for KPSS to determine whether they are stationary or not >> yes so the answer is high correlation does not refer to causation that's is the main crux of this like even though two two stocks can be highly correlated but that does not mean we can use it for pair trading right which means high correlation does not signify causation. So what you generally do is you perform stationerity test on both the stocks and if both the stop stocks are stationary then you perform this statistical test called um uh uh test uh angle grner >> angle grner angle gr >> yeah some test like that yeah >> testing for residual units so that's >> yeah but some I remember one of the student was asked this question does uh so the question was not on pairs trading. It was more on correlation and causation like to basically if you could uh define what is correlation, what is causation and does one automatically refer to the other something on those lines basically >> like co-integration correlation and uh >> causation >> causation grand causation or transer causality >> yes because see uh I remember one of this uh student was uh see if you go with if who are targeting Millennium or all these hedge funds, right? They use uh time series modeling left, right, center, you know, left, right, center they use. So that's why it's very important for them to make sure you understand all these terms. Okay. All right. Uh going on to my next question.

[00:35:58]Just give me one second.

[00:36:08]Okay, let's say your model uh you build this uh time series model AR, MA, ARMA, whatever it is, right? And uh how would you um uh how would you tell if the model is predicting well or if the model is not performing well? what all what all things or what all metrics would you use to tell if the model is performing well and how would you even say if the model you know like what's the thing you would do?

[00:36:36]>> So there are couple of metrics this m like matrices we use to evaluate our model. So one is mean absolute error and the the another one is mean square error. But there is one root square mean root mean square >> and one is R square and one is mean absolute percent >> and another is AIC and BIC >> which are used to understand which model we'll be using but again yeah AIC and BIC is also now the thing is what we do in the industry is we create more like band gaps. So let's say if your RMS is between 0 to 0.25 25 your model is pretty well. If your RMS is 0.25 to 0.5 your model is moderate. But if the RMS is greater than.5 your model is performing poorly. So you create this color bands. So when you and this color bands it's not very specific. It's not like oh the range is 0 to 0.25. No the range depends on what you are trying to model. So how do you even come up with this uh range? Of course, right? How would you determine this range? You do back testing.

[00:37:47]>> Yeah.

[00:37:48]>> Basically, what you do is you let's say you take certain ranges because you only need to tell the model validation what kind of ranges are you trying to put in.

[00:37:56]It's not like oh you you can just take whatever it is. You you go tell the model validation these are the band gaps we are trying to perform and it should not be um something very uh like oh I'll take 0 to one. No, it should be also industry standard. You know something what industry is following. So, but yeah, this is one thing you would uh face when you actually do the modeling.

[00:38:21]Um, okay.

[00:38:23]How would you uh select an optimal ARMA model? What all things you would test?

[00:38:31]>> ARMA. Yeah, >> we would test the lo likelihood ratio and the uh AIC bic means if you are comparing the different models of ARMA >> correct. So AIC, BIC, log likelihood, adjusted R square or R square in general for five matrix and then if you are looking for the forecasting see one is model testing like which model fitting one part is model fitting which model is fitting well that you understand from this AIC VIC log likelihood or and then the next step is forecasting.

[00:39:02]So you have to look at both the ends which if the model is fitting well because sometimes the model will fit well but will not perform good in forecasting which is a classic example of overfitting >> right it will fit well but not good for forecasting so that's why you need to look at both the parameters all right so now uh can you explain what is arch and gel Yeah. So, AR stands for auto reggressive conditional heteroscasticity.

[00:39:37]>> Uh, which is based on the consideration that the present value present value of the volatility term of a time series.

[00:39:45]>> Mhm. Okay.

[00:39:46]>> Is actually a function of the square of the past residual terms.

[00:39:51]>> Okay. So sigma square t is equal to omega + beta epsylon square tus 1 plus epsilon t. So this is arch model for garch. Garch is a generalized auto reggressive conditional heteroscalasticity model.

[00:40:06]>> Okay.

[00:40:07]>> Which also takes into consideration the past values of the volatility terms. So it is sigma square t is equal to a constant c plus alpha into epsilon square t - 1 plus beta sigma square tus 1. Perfect. Now >> and it is based on the assumption that the volatility is not a constant over a period of time unlike AR and MA models.

[00:40:30]>> Okay. Quick question before you ask is how is these time series models ARMA ARMA different from this volatility based models?

[00:40:42]These models uh assume that the variance is constant over time that is it is not continuously growing but uh the arch and gas model assumes that the variance fluctuates. Perfect perfect answer. So time series models arma anything like that right it assumes that your this um variance is constant mean is constant right hetroscadastricity means changing variances. So that's why arch g or any volatility based models they are they they mean what they it is changing the volatility or variances the variance is not constant and that is the main difference. So that's why you won't see AR model being used for volatility modeling. No if you use it the fundamental itself is wrong right because AR is used for constant variance but here volatility is always changing.

[00:41:38]Okay your question. Yeah, >> my question was uh like uh P when you were explaining the arch and the GACH model like uh you said about the arch model that it has that residual term to >> standardize or you can say innovations.

[00:41:55]Do do we add that? Because like if we add any kind of uh uh residual term to that like it would kind of be similar to a garch equation also because in the garch equation we have alpha beta over there with the residual terms and in the arch equation we only have one term over there with the baseline. It's kind of like the MA model or AR model just a volatility we take.

[00:42:22]Uh I'm a bit confused like uh I might be remembering the equation wrong. I'm just trying to confirm like uh what I'm trying to >> I think in the arch we don't have past variance but in GA we have both the ones squared errors and past variance as well.

[00:42:39]>> Yeah that's what I thought like I think we added that resol we should remove that.

[00:42:45]>> Yeah in ours we don't have the past variant that's why like we used generally guard for the volatility modeling. Only difference is that GA captures the path variance as well but arch only has square residuals.

[00:42:56]>> Gar vance >> the definition was absolutely correct.

[00:43:00]>> Okay. Great. Now I guess these are certain questions which you will be uh you know having in all your in if if it's if it's a time series interviews these are a bunch of questions you will be asked. Now there are certain takes which are uh you know conclusion which I want to do from this whole uh session.

[00:43:20]See first is even though if you know a concept let's say I know konag knows the concept but if you are not able to translate then getting reject is very high in US if you are not able to answer one or two interview questions you are gone I'm sure you you might have already seen it but if you have not this is the reality and thing is we are not just targeting $100,000 job we are targeting 130 $150,000.

[00:43:51]So if your target is that you need to make sure you know everything right be it correlation causality any vector auto regressive I've not touched that topic but I hope you I hope you understand what I'm trying to say. So first thing is making sure you understand the definition. I guess my [clears throat] very first question was what are the what is time series modeling and different components. Very simple answer trend seasonality this uh cyclical pattern and random fluctuations but if you're not able to use the terms well interviewer won't understand what you're trying to say.

[00:44:31]It's something like this. Uh you know we we know all of us know this term called value at risk right we [clears throat] we would not always say oh what's the potential loss what's the potential loss what we'll say is value at risk >> in a very similar fashion when you are doing this time series modeling we'll refer to the term cycle trend seasonal pattern stuff like that okay second thing is uh so first thing is making sure you articulate things well second thing is a great thing you can do in all your questions is to add an example. So when you add an example the interviewer understand you really know the concept well like I'll give you one um I'll give you one scenario I asked this question uh how do you convert a non-stationary data into stationary what Ishan answered was well like you do uh let's say you take uh returns simple return or log returns it's a it's a it's the right answer but is it a complete answer the answer is no it's not a complete answer because there are bunch of ways he just covered one part of it. So until unless he covers everything I'm not satisfied as the interviewer okay so these are two things first is make sure you understand each and every term and you are able to translate it to the interviewer second is adding certain examples will really help you in you know making sure you have a better knowledge than other folks. Okay. So I guess uh that was all for time series modeling. Uh again you have like 20 25 questions not more than that which are asked in these kind of settings. Um again uh I guess um we'll uh I guess the next topic I'll I'll just post it in the group uh which we'll practice next week.

[00:46:23]But again for this uh it was all any doubts you have.

[00:46:27]uh do they ask different types of GA models or the models that are working in the until you have written it they'll not ask >> they wouldn't ask like I got or all these models >> no so GG go I got exponential G they'll not ask unless you specifically written it >> and [clears throat] what kind of questions can they ask because if we are trying to include time series modeling we have like we might include GA model or like GGR >> yeah I'll tell you I'll tell you. So let's say you have this gaj or ggraj model in your portfolio.

[00:47:02]>> They'll understand what is what are the steps being followed. First thing how did you perform the modeling? What are the results? How did you look at the residuals? Did you perform any kind of statistical test on the residual? Did you perform any statistical test on the distributions of the variable? You know instead of me stating oh I used a gach model. Gaj assumption is it assumes a normal distribution but it's is stocks are stocks normal distributed? The answer is no. So utilizing GH would not help for risk management or whatever volatility modeling you are doing.

[00:47:37]>> So first thing is you do a statistical test to understand what distribution the data is. So eventually what they'll ask is to complete workflow not just okay let's take G and just ask me a bunch of questions. No that will not happen. They'll ask complete workflow and then what worked what did not work and what are the limitations or challenges you faced.

[00:48:00]So that kind of questions you they can ask you and then what is the next step let's say oh you model volatility but then how are you utilizing the volatility so you have spy options right so you can use this implied volatility in SPI options because in that way you can at least come up with the option pricing correct I'm just giving you examples >> but eventually they'll not just ask you okay what is so they'll ask What is GAGE? What are the components of Gajge?

[00:48:32]How is Gajge different from GGR gaj?

[00:48:34]What additional parameters you add in the mathematical equations of the GGR gaj? They'll ask you these because you have listed all these. What extra they can ask you is about the distributions about the residual testing you performed. So that is also important.

[00:48:50]Okay. Any any other questions anyone has?

[00:48:57]Anything?

[00:49:02]No.

[00:49:03]>> Okay. Perfect. So, let's meet uh next week. Uh I'll tell the uh the topic in the group and uh let's practice uh next week. Okay.

[00:49:14]>> All right. Thank you so much.

[00:49:16]>> Yeah. May please call weekend.

[00:49:23]>> Okay. I know. Um Okay. Okay. I'll do next time little early. Okay. I'm so sorry. Let's do a little early next time. Okay. All right. Anything else?

[00:49:35]>> No.

[00:49:36]>> Okay. Perfect. Sure. Take care. Let me stop the recording. Let's meet.