lfarlima / Time-Series-Linear-Regression-Analysis

Time Series and Linear Regression Analysis

Return Forecasting:

• The Yen Futures Settle Prices plot shows an upwards trend long-term.
• In the short-term, the price seems to be volatile.

Based on your time series analysis, would you buy the yen now?

• The model demonstrates a consistently high confidence interval, so we can conclude the GARCH model is a good fit.

• The beta coefficient (0.95) indicates the slight increase in volatility is expected in the long-term, while the alpha coefficient (0.04) suggests a historically stable return on asset; the alpha and beta combined (0.99) suggests the stable volatility of this asset will persist in the long-term.

Is the risk of the yen expected to increase or decrease?

• Based on the upward trend in the forecast plot, the exchange rate risk is expected to increase slightly over the next 5 days.

Based on the model evaluation, would you feel confident in using these models for trading?

Forecasting Returns using an ARMA Model:

• The ARMA model is not a good fit, since the p-value (0.422) is greater than the significane level of 0.05.

• Therefore, the coefficient of the autoregressive moving average is NOT statistically significant, and should NOT be kept in the model.

Forecasting Settle Price using an ARIMA Model:

• The ARIMA model forecasts that the Japanese Yen will increase in the near term. However, the autoregressive term has a p-value (0.652) that is greater than the significance level of 0.05.

• Therefore, the autoregressive term from this model is NOT statistically significant, and should NOT be relied on to forecast Yen futures accurately.

Volatility Forecasting with GARCH Model:

• The GARCH model results in a p-value (0.00171) that is lower than the significance level of 0.05. Therefore, this model is statistically significant. The model demonstrates a consistently high confidence interval, so we can conclude the GARCH model is a good fit.

• Further analysis using the exponentially weighted moving average (EWMA) to determine if investment in this asset is recommended, since the calculations may be diluted by the distant (less relevant) data.

Regression Analysis:

• *The out-of-sample RMSE (0.415) is lower than the in-sample RMSE (0.596). A lower RMSE for training data (in-sample RMSE) indicates a good fit, yet this model has a higher in-sample RMSE. In other words, the model performed better on the testing data (out-of-sample RMSE) which it had never seen before. Therefore, I would NOT recommend using the predictions from this model.