Research Officer Exam Special | Syllabus Updated | Statistics | Time series Analysis

Added: 2026-05-12

[00:00:00]Welcome back all of you.

[00:00:12]Module eight time series of time series. Analysis of ACF and PACF moving average MA and auto reggressive moving average MA and AA time series models.

[00:00:54]Time series.

[00:01:15]First topic ACF autorelation function.

[00:01:22]ACF autorelation function between a time series and its own lag values.

[00:01:47]autorelation function.

[00:01:52]So row of k is equal to and coariance of xt minus xtus kag divided by variance of x of treoration by variancorrelation functionariance of x of tus by variance of xorlation autocorrelation measure function measures the correl correlation between a time series and its own lagged values.

[00:02:30]shows linear dependence between observations at different observations.

[00:02:47]in the values between minus1 and + one helps identity m of process moving average function indicates a behavior auto reggressive behavior shortcut Q moving average model identification detecting seasonality and checking randomness. So these are the uses of ACF autocorrelation function in the can model identification detecting seasonality and checking randomness.

[00:03:49]Okay. Then we are moving to the PACF.

[00:03:53]PAF means partial autocorrelation function.

[00:03:59]ACF and PACF. ACF means it is autocorrelation function and PACF means partial autocorrelation function.

[00:04:11]Correlation between X of T and X of T minus K. After removing the effect of intermediate intermediate correlation partial autocorrelation function shows direct relationship at relirect correlations.

[00:04:53]Sharp cut off after cut off.

[00:05:22]Moving average behavioral direct moving average identification.

[00:05:43]Autoressive identification behavior tales of autoressive cuts of autoav.

[00:05:57]So these are the summary comparison of ACF and PACF.

[00:06:02]ACFlirect moving average.

[00:06:28]Okay.

[00:06:30]Next.

[00:06:32]Auto reggressive model. Autoressive model. An auto reggressive model expresses current value as a function of past values.

[00:06:46]Function express auto reggressive model. Auto reggressive model expresses current value as a function of past values.

[00:06:59]values auto reggressive model that is x of t is equal to 51 of x of t minus values plus 52 of x of t - 2 + 5 of x of t minus p + epsilon t i 51 52 etc and parameters.

[00:07:40]It is a type of signal or sound that contain all frequencies in equal intensity.

[00:07:57]range.

[00:08:04]It's a random signal with no predictable pattern.

[00:08:17]ience power is evenly distributed across frequencies.

[00:08:36]It is often used in signal processing, statistics and acostics. Example, the static sound from an untuned radio.

[00:08:51]Background noise used for sleep or concentration.

[00:08:55]Random fluctuations in electronic circuit.

[00:09:16]baseline model.

[00:09:40]Auto regressive model X of T 51 of X of T -1 + 5 2 of X of T - 2 plus etc plus 5 P of X of T minus P plus epsilon T regressive model depends on past observations roots of lie outside cuts off ACF.

[00:10:37]Okay. Then next one is moving average model.

[00:10:49]Then moving average and moving average model expresses current value as a function of Moving average model and moving average model expresses current value as a function of past errors.

[00:11:26]Moving average model depends on past ACF and ACF cuts off and ACF tails off of the parameters constants theta1 epsilon t - 1 + etc plus theta epsilon T minus Q moving average modelress moving average moving average combination.

[00:12:44]AM modelressive moving average.

[00:12:51]A R MA auto reggressive moving average model. It is nothing. It is the combination of auto reggressive and moving average model.

[00:13:04]combination 1 x of t - 1 + etc plus 5 of 5 p x of t minus p plus epilon moving average theta tus 1 plus etress moving average used for stationary time series.

[00:13:55]time.

[00:14:04]Persistence means in the case of effects moving average.

[00:14:31]model.

[00:14:33]Auto reggressive integrated moving average.

[00:14:38]Auto reggressive integrated moving average extension of ARMA for non-stationary data predressive degree of difference moving average moving average order of equal mus the whole dx of t is equal to a m of p q where b is the back shift operator back shift operator auto reggressive integrated moving average model for 1 - b the whole dx t is equal to p of q and auto regressive model 1 - b of d 1us b the whole power d xg is equal to p q where d is the back shift operator makes non-stationary data stationary by Differencing nonstenkins approach identification station analysis. Identification, estimation, diagnostic checking and forecasting.

[00:16:49]steps.

[00:16:51]Identification, identification, estimation, uh diagnostic checking and forecasting and forecasting.

[00:17:09]Steps in modeling, modeling, identification, estimation, diagnostic, forecasting, important concept depends only once.

[00:17:54]Time series is stationary. If mean is constant, variance is constant. Coariance depends only on litakity.

[00:18:13]Fore.

[00:18:33]Okay.

[00:18:35]What are the applications? application, economic forecast, stock price analysis, weather prediction and signal processing. These are the main applic Diagnostic tools function. PS means partial autocorrelation function. Diagnostic tools moving average means autoressive moving average autogressive moving average.

[00:19:50]NCQ.

[00:19:52]White noise is defined as a process.

[00:19:54]Well, White noise is defined as a process where is zero mean autoorrelation.

[00:20:32]Autocorrelation.

[00:20:34]No autocorrelation.

[00:20:37]The autocorrelation function of white noise is autocorrelation function of white noise. Right now is an autocorrelation function.

[00:20:49]Autocorrelation function.

[00:21:02]ACF = 0 for all ls k= z 1 4 lag zag autocorrelation function zagoration function autocorrelation function of white Noise.

[00:21:40]C for all nonzero answer. Which of the following is true for white noise? White noise completely.

[00:21:58]It's pure white noise is pure randomness with no structure. White noise option C it is completely random. Option C. It is completely random.

[00:22:15]White noise processes always non-stationary weekly stationary periodic deterministic white noise process is weekly stationary.

[00:22:39]weak stationary. So answer if x follows function.

[00:22:57]No correlation correlation correlation between time points.

[00:23:15]by variance between different time points.

[00:23:29]Different time points which process is an exam of white noise.

[00:23:34]right now is an exam.

[00:23:38]Yes. Random shocks in stock prices.

[00:23:44]Random shocks in stock example of white noise. White noise.

[00:23:58]The variance of white noise processes.

[00:24:00]White noise process.

[00:24:10]The variance of white noise process is constant noisecessant.

[00:24:17]Which of the following is not a property of white noise?

[00:24:26]No autocorrelation.

[00:24:29]Autocorrelation exist. So autocorrelation.

[00:24:38]No autocorrelation.

[00:24:40]No autocorrelation.

[00:24:52]often denoted by the spectral density of white noise.

[00:25:15]Spectral density of white noise. White noise density. Right now spectrum that means it is constant.

[00:25:28]The spectral density of flat flat.

[00:25:35]Which statement is correct?

[00:25:38]White noise has predictable values.

[00:25:41]White noise has autocorrelation. White noise is purely random. And white noise has a train.

[00:25:49]purely random. So that is the statement is purely random that is correct.

[00:26:10]Purely random noise is purely random.

[00:26:15]If a time series has zero autocorrelation at all non zero autocorrelation in time series modeling white noise is used to represent time series model.

[00:27:00]Which condition ensures white noise is conditional distribution?

[00:27:13]Normal distributional distribution follows normal distribution only then it is for white noise the observations are dependent independent and identically distributed. deterministic and periodically.

[00:27:50]So option B independent and identically distributed mean often denoted by epsilon. These are the important tips related to the and then white noise. noise related to important mean zarian constant AC pure randomness often by t. Then the autocorrelation function meas measures the autocorrelation function ACF measures.

[00:28:44]Correlation between a series and its lagged values. Correlation between a series and its lagged values. Then the value of ACF lies between always lies between ACF. The autocorrelation at Lag Z is ACF autocorrelation function zero perfectlation perfectlation with itself with itself. Perfect correlation with itself.

[00:29:35]Partial autocorrelation function measures. Partial autocorrelation direct correlation removing intermediate lags. And then direct correlation removing intermediate lags.

[00:29:50]Which of the following is true for partial autocorrelation function?

[00:29:55]Partial autocorrelation function.

[00:30:00]removes effects of intermediate lags.

[00:30:04]Removes effects of inate lags for an auto reggressive process. The PF already cuts off after lag P cuts off after lag.

[00:30:26]Okay. So uh up to then thank you all. We can meet with another topic as early as possible. Thank you.