[SOLVED] Indr 450/550 homework 2

1. (40 points) Forecasting Coffee Prices (monthly average price index of
coffee in commodity markets as reported by the IMF commodity price
data portal). This continues from the first HW.
(a) Plot the data and visually assess whether there is significant trend
and seasonality.
(b) Check the ACF and PACF plots after detrending and deasonalizing (if necessary). Check whether there is significant AC visible.
(c) Fit an ARIMA model to the whole data set based on the autocorrelation structure and the patterns (trend, seasonality etc.).
Explore the significance of the fitted coefficients, the residual diagnostics and assess its performance by calculating the MAE,
MAPE and RMSE.
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(d) Experiment with a different ARIMA model for comparison.Explore
the significance of the fitted coefficients, the residual diagnostics
and assess its performance by calculating the MAE, MAPE and
RMSE. Compare with the previous model.
(e) Separate the data into a training set and a test set (first 70 to
80 % of the data should be the training set and the remaining
data test set). Fit the two models above on the training set and
compute the forecast errors on the test set.
(f) Your report for the exercise should include a table similar to the
one below.
2. (40 points) We had looked at the monthly Australian Beer Production
data. This time we investigate the quarterly production data starting
from the first quarter of 1956 to the second quarter of 1994.
(a) Plot the generated observations.
(b) Fit a SARIMA(0,1,0)(0,1,0,4) model to the whole data (i.e. seasonal differencing of 4 quarters and first order differencing). Explore the significance of the fitted coefficients, the residual diagnostics and the error performance. This could be a benchmark
model for other comparisons.
(c) Detrend and deseasonalize the data. Plot the Auto-Correlation
Function and the Partial Auto-Correlation Function of the detrended and deseasonalized data.
(d) Based on the ACF and PACF, fit a SARIMA model to the whole
data that has some AR and MA coefficients. Explore the significance of the fitted coefficients, the residual diagnostics and assess its performance by calculating the MAE, MAPE and RMSE.
Compare with the previous benchmark model.
(e) For the best model you found, find a one-quarter ahead forecast
for quarter 155 (using all data available until the end of quarter
154) and report the 95 % prediction interval for your forecast.
(f) Separate the data into a training set and a test set (first 70 to 80
% of the data should be the training set and the remaining data
the test set). Fit the two models above on the training set and
compute the forecast errors on the test set.
(g) Your report for the exercise should include a table similar to the
one below.
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Table 1: Summary of Results for Exercises 1 and 2
Method Spec. RMSE (Train) RMSE (Test)
Benchmark (from HW1) –
Model 1 ϕ1 =, θ1 =, etc.
Model 2
Model 3 (if any)
The model specification includes the ARIMA specification (i.e. ARIMA
(1,0,2) or SARIMA(1,0,2)(0,1,0,4)) and the fitted coefficients.
3. (20 points) Fit ordinary linear regression models to the quarterly Australian Beer Production data.
(a) Fit a linear regression model that uses seasonal dummies as predictors (note that there are four quarters and three corresponding
seasonal dummies are needed). Check the R2 and the significance
of the coefficients and compute the MSE.
(b) Fit a linear regression model that uses seasonal dummies and a
linear trend term as predictors. Check the R2
, adjusted R2 and
the significance of the coefficients and compute the MSE.
(c) For both of the models in part a and part b, find a one-quarter
ahead forecast for quarter 155 (using all data available until the
end of quarter 154) and report the 95 % prediction interval for
your forecasts.
(d) Your report for the exercise should include a table similar to the
one below.
Table 2: Summary of Results for Exercise 3
Method Spec. R2 RMSE
Benchmark (from HW1) –
Model 1 β0 =, β1 =, etc.
Model 2
Model 3 (if any)