Multivariate Time Series Analysis

Instruction: Explain the Vector Autoregression (VAR) model and its application in forecasting multivariate time series data. Discuss how to determine the optimal lag order and interpret the results.

Context: This question tests the candidate's knowledge of VAR models, which are used for forecasting interconnected time series data. Candidates must explain the theory behind VAR models, steps to estimate the model including selection of the optimal number of lags, and how to interpret the results of the model in the context of forecasting and causality between multiple time series.

Updated

Example Answer

A VAR models each variable using lags of itself and the other variables in the system. For example, I could compare a joint model of demand and bookings with separate forecasts, provided their histories are aligned and available at the forecast date.

I would check whether a stationary VAR is appropriate. Cointegrated nonstationary levels may call for a vector error-correction model instead of discarding their long-run relationship through differencing. I would choose candidate lag orders using information criteria, then check stability, residual dependence, and forecast performance. More variables and lags mean many more coefficients. Impulse responses also need careful identification: a fitted lag relationship is not, by itself, proof that changing one business input causes the forecasted response.

Make it your own

Choose a small set of variables and explain why their joint history could add predictive value.

Why this works

It includes both the joint model and the conditions needed to interpret it.

Follow-up to practice

How would you handle cointegrated variables?

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