ICAR AICE-JRF/SRF Time Series Analysis: practice questions

1 · Components of time series and classical decomposition · easy

Pig prices in a region rise and fall in waves lasting three to four years, driven by farmers expanding and cutting herds in response to past prices. In classical decomposition this movement is best classed as:

1. Cyclical variation
2. Secular trend
3. Seasonal variation, because it repeats in a regular way
4. Irregular variation caused by unpredictable shocks

2 · Components of time series and classical decomposition · medium

A plot of monthly onion arrivals shows the seasonal peaks and troughs growing wider as the general level of arrivals rises over the years. Which model is most appropriate for decomposing the series?

1. A multiplicative model, Y = T x S x C x I
2. A model with trend only, since the seasonal pattern is not constant
3. An additive model fitted after removing the trend by first differencing
4. An additive model, Y = T + S + C + I, with fixed seasonal amounts

3 · Smoothing: moving averages and exponential smoothing (Holt-Winters) · medium

Why do forecasters often prefer a damped-trend version of Holt's method for horizons of several years?

1. It always gives narrower prediction intervals than Holt's method
2. Its long-range forecasts level off instead of rising for ever
3. It removes the need for a level equation in the model
4. It makes the method equivalent to simple moving averages

4 · Stationarity, autocorrelation and partial autocorrelation functions · easy

For a series of 100 observations, what are the approximate 95 per cent limits for a sample autocorrelation under the hypothesis that the series is white noise?

1. +/- 0.100
2. +/- 0.196
3. +/- 0.392
4. +/- 0.020

5 · Stationarity, autocorrelation and partial autocorrelation functions · easy

The sample ACF of a monthly price series starts near 0.95 and declines very slowly and almost linearly over 30 lags. What should the analyst do first?

1. Difference the series
2. Fit an MA(30)
3. Fit an AR(1) model to the levels at once
4. Conclude the series is white noise and stop

6 · Stationarity, autocorrelation and partial autocorrelation functions · medium

A stationary series has rho(1) = 0.6 and rho(2) = 0.5. What is the partial autocorrelation at lag 2?

1. 0.360
2. 0.140
3. 0.500
4. 0.219

7 · Stationarity, autocorrelation and partial autocorrelation functions · medium

Why is a random walk, Y(t) = Y(t-1) + e(t) with e(t) white noise, not stationary even though its expected change is zero?

1. Its variance grows with time
2. Its errors are correlated with one another
3. Its mean rises in a straight line with time
4. Its first difference is a non-stationary series

8 · AR, MA and ARMA processes · easy

The process Y(t) = 4 + 0.6 Y(t-1) + e(t) is stationary. What is its mean?

1. 4
2. 10
3. 2.4
4. 6.67

9 · AR, MA and ARMA processes · easy

The sample ACF of a stationary series has one significant spike at lag 1 and nothing beyond, while the PACF decays gradually. Which model does this suggest?

1. ARMA(2,2)
2. AR(1)
3. AR(2)
4. MA(1)

10 · Box-Jenkins ARIMA: identification, estimation and diagnostic checking · easy

What is the order of the stages in the Box-Jenkins approach to model building?

1. Identification, estimation, diagnostic checking, then forecasting
2. Forecasting, estimation, identification, then diagnostic checking
3. Estimation, identification, forecasting, then diagnostic checking
4. Diagnostic checking, identification, estimation, then forecasting