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# Multivariate Arima | What Are Multivariate Time Series Models || Data Science

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## What Are Multivariate Time Series Models || Data Science

Transcript:

Hi, in this video. I’m going to talk about. What are the multivariate time series models? Okay, in a in a channel, We have talked about the univariate time series model, and we all also talked about the structural models, okay. So what do you mean by? Structural models are the regression based models, and we also talked about the forecasting models like the univariate time series model and one of the questions that is often asked is. How are these two models related? Can we have models which combines the univariate time series analysis and the structural models? Okay, and that question cannot be answered by and without understanding what a multivariate time series analysis. Okay, so let’s try to understand what we learned up in a new maritime SIS models and water structural models and, however, is combined in multivariate time series, so in anyway, a time series. We learnt that if a series. YT is stationary series. It can be the future values of. YT can be it. Can we can forecast the future value of the time series? YT by taking its past values, okay, and then there will be an intercept and there will be a flow coefficient and the error term has to be white noise, right, so YT is the stationary time series. It is Olivia Combination of its past values. YT minus 1 and YT minus 2 and so on, so this is basically a AR 1 model it. We can also have a 2 model by including more lags, right air to Air 3 and so on, we can also have these error. Terms included that by including the moving average terms, so we can have ma model and we can combine these models to form the ARMA type ones right, both the flags of the time series at the same time, the error terms, right, and if it is not a stationary, we can take the difference of that, you know, build what is known as the ARIMA type right first in, take the difference and then apply the ARMA class or models to it, and then it becomes our image class of model, so that’s all about the univariate time series analysis. So what are structural models in structural models? We have dependent variable, and then we have independent. Variables dependent variables are in most times different from the independent variables. I mean, there are different, totally different variables. Okay, one example, could be. Let’s say we are finding out. The unemployment rate so unemployment rate is the dependent variable and we are building a model just to know how inflation inflation in a particular country affects the unemployment rate. Right, so this is a typical structural model. It’s a regression linear regression model wherein we’re trying to see how inflation in the country effects the unemployment. How are they related or can we focus the unemployment rate based on inflation, the value of inflation and then we are trying to find out or try to find out the regression estimates like beta naught and Beta 1 which are the intercept and the slope coefficient’s, all right, so that to be most structural models, are we do not have a time component here? We do not have a time component for, you know, For a particular, you know, we can have unemployment rate for different states in let’s say the US. Or India, or in different countries in Europe, so these are like you know, unemployment rate in different states in India and we have, okay, let us say. These are unemployment, it’s in different countries in Europe and inflation rates in different countries in Europe. Okay, and that’s how you build build a model structural model, but we normally do not have a time component in structural model, right, we do not have time series variables, variables with change with time and one of the reasons you know, time component of variables with time, which vary with time and not present in structural model is because of the problem of autocorrelation. So the problem of what? Oh, correlation is is a typical case in which the the errors of regression models are correlated with each other and that it’s seen. Because if we keep on if you use a time varying variable, its values will be correlated over time right, and that will impact the error terms and the error terms will even – will. Also, you know, be correlated and that valid one of the Assumption in ordinary least square estimation that is the errors has to be uncorrelated or errors, so not so any pattern there has to be totally have uncorrelated with each other. The problem autocorrelation is found out in such cases, right, and hence normally there has to be a lot of changes in the model. Specification has to be made in order to do the regression with time varying independent variables. Right, so these are this basic differential difference between any variate time series and sexual models, where it’s either very a time series only uses the past values nothing else structural models on the other hand do not use the time reading time varying independent variables. It’s rather includes variables with change with cross section. Okay, we change with cross section. As in. It could be a countries it could be states. It could be different groups, right, so X can be for different countries. Inflation can be four different countries on employment can be four different countries and so on. But normally inflation, unemployment and inflation for a particular given time period of changing time period is not taken right. And if you know only the time bearing pattern is something that is of interest. Then one goes for the in value times in models. The multivariate time series model combines. This is two things, okay. Multivariate time series models include the lags of the same time series. It also includes the lags of an independent variable or a factor. Okay, so the specification includes both multiple variables, and it also has in time series component and hence is this class of models are known as the multivariate time systems. So here is the specification. So this is the specification that you can see. YT is is a linear combination of its pass values. Its own lakhs. Plus, the past values of another independent, variable X okay and both YT and XD are stationary time series stationary time series and ET. The error term is is white noise. Okay, alright, so what I have seen here? Is that that the specification in the model specification is a not only having the lags of the same variable same variable interest. It also has a lags of some other variable, which is supposedly supposed to be interest related to. YT may be XT in in some ways affecting YT. Okay, so that is a structural component, right, so we have now sort to say independent variable rate and the question is does the estimation is same as what is there in the structural models. Right we can we use. Ols, can we use the same type of maximum likely the way we used to use for structural models with the assumption? The classical linear regression assumption. Hold in this case now. These are all complicated questions to be answered and we’ll see in another video where well we will discuss about the estimation procedure for a multivariate time series, one another popular time series model, which is multivariate. Is the vector autoregression. Okay, the vector. Auto Regression, Okay, a popularly known as a bar model. Okay, so the bar model is some form of multivariate time series models and we’ll see how we can estimate a bar equation, a model which is specified using vector ghetto regressions. Thank you for watching this video and please subscribe to our Channel, thank you.

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