Answered: Explain the various concepts & tools of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Explain the various concepts & tools of regression with time series data?

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Step 1

A time series can be decomposed into three components: the trend (long term direction), the seasonal (systematic, calendar related movements) and the irregular (unsystematic, short term fluctuations)

Time series regression is a statistical method for predicting a future response based on the response history (known as autoregressive dynamics) and the transfer of dynamics from relevant predictors.

Time series regression is commonly used for modelling and forecasting of economic, financial, and biological systems.

Usually the errors in time series data is usually exhibit some type of autocorrelated structure. By autocorrelation we mean that the errors are correlated with themselves at different time periods.

Some of autocorrelation in time series regression is from failure of the analyst to include one or more important predictor variables in the model.

Correlation over time (Serial correlation): The correlation of a series with its own lagged values is called
autocorrelation or serial correlation.

The first autocorrelation of

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First autocovariance of

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Autoregressive (AR) model : A natural starting point for a forecasting model is to use past
values of Y (

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) to forecast

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An autoregression is a regression model in which Yt is regressed against its own lagged values.

The number of lags used as regressors is called the order of the autoregression.

In a first order autoregression,

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is regressed against

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The first order autoregressive model AR(1) is

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And

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order autoregression

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is regressed against

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The

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order autoregressive model AR(p) is,

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When p =0, it means that there is no auto-correlation in the series. When p=1, it means that the series auto-correlation is till one lag.

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