Forecasting Time Series Assignment 2022

Running head: FORECASTING TIME SERIES 1
Forecasting Times series
Name
Institution

FORECASTING TIME SERIES 2
Forecasting Times series
Task 1
Data Exploration
The codes used in the analysis are included in the appendix. The first step involved
plotting series to allow for visual inspection of the key features (Kohli & Singal, 2014). The
figure 1 shows time plot of solar radiations reaching the ground.
The observation from figure 1 are: (1) There is no trend component since the observations do
not seem to increase or decrease over time. (2) There seems to be seasonal component with a
cycle shorter than 12 months. (3) The variance in the data seems to be constant over time.
However, to verify these observations we decompose the series into its various components.
Figure 2 shows plot of the components of solar radiation series. Now that the series is
stationary, we can estimate regression models using the data.

FORECASTING TIME SERIES 3
From figure 2 seasonality exist in the series, but the data does not have trend. The next step is
checking for stationarity of the data using the Dickey-fuller test. The test is based on the null
hypothesis that the series is non-stationary (Kohli & Singal, 2014). The estimated D = -
6.1434 (p-value < 0.01) indicating that the series is stationary.
Time series regression model
Using dLagM package we obtain the model with the smallest mean squared error (MASE)
(Kohli & Singal, 2014). From the analysis, the optimal model with least MSE is dlm model
with q = 13. The figure 3 shows the models fitted.

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Figure 3: Output of the Finite Model
Next, we estimate the optimal model using q=13, k=3 and make forecasts based on the
model. The model is fitted using polyDlm function from the dLagM package. We are not
interested on the parameter estimates we only need the model for forecasting the series. The
forecasts are obtained using dlmForecast function to make an auto ARIMA. Figure 4 shows
the forecast from time series regression model.
Dynamic Linear Models