Choose a suitable time-series model for a given investment problem and give reasons for the choice
The idea
Choosing a time-series model follows a sequence. Understand the question and plot the data. If there is no seasonality or structural break, try a trend model and check its residuals for serial correlation; if they are correlated, move to an AR model. Before that, make the series covariance stationary, by differencing it, taking logs first if it grows exponentially. Fit an AR(1) and test the residual autocorrelations, adding lags or a seasonal lag until none is significant. Then test for ARCH and correct if needed. Finally compare models on out-of-sample RMSE. When two series are involved, check unit roots and cointegration. The trap is modelling levels that are not stationary.
In the app: 3 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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- Work out a trend forecast for a time series, whether fitted as a linear or a log-linear trend, from given trend coefficients, and judge the result
- Explain what decides the choice between a linear and a log-linear trend for a given series, and assess where trend models fall short
- Explain why a time series needs to be covariance stationary and what it means when a series lacks stationarity
- Set out how an order-p autoregressive (AR) model is built and, from its fitted coefficients, work out forecasts one and two periods ahead
- Explain how residual autocorrelations let you check whether an autoregressive model suits a time series
- Say what mean reversion is and work out the level a series tends to revert to
- Distinguish forecasts made within the sample from those made outside it, and rank time-series models by forecast accuracy using root mean squared error
- Explain why time-series model coefficients can be unstable
- Set out the features of a random walk and how it differs from a covariance stationary process
- Explain what unit roots mean for time-series work, when they tend to arise and how to detect them, and show how to transform a series with a unit root so that an AR model can be used on it
- Set out the stages of testing a series for a unit root (nonstationarity) and explain how the test connects to autoregressive models
- Explain how to detect and adjust for seasonal effects in a time-series model, and work out and explain a forecast from an AR model that includes a seasonal lag
- Say what autoregressive conditional heteroskedasticity (ARCH) is and show how ARCH models help forecast a time series' variance
- Explain how to check time-series variables for cointegration and/or nonstationarity before putting them into a linear regression