Times Series Analysis and Linear Regression Modeling

In this exercise, I've test the time-series tools in order to predict future movements in the value of the Japanese yen versus the U.S. dollar. I've loaded historical Dollar-Yen exchange rate futures data and applied time series analysis and modeling to determine whether there is any predictable behavior. I've built a Scikit-Learn linear regression model to predict Yen futures ("settle") returns with lagged Yen futures returns and categorical calendar seasonal effects (e.g., day-of-week or week-of-year seasonal effects).

Time-Series Forecasting notebook completes the following:

1. Decomposition using a Hodrick-Prescott Filter (Decompose the Settle price into trend and noise).
2. Forecasting Returns using an ARMA Model.
3. Forecasting the Settle Price using an ARIMA Model.
4. Forecasting Volatility with GARCH.

Findings:

1. Based on your time series analysis, would you buy the yen now? - Overall trend Yen/ USD is upward. Prices are increasing so i would buy Yen.
2. Is the risk of the yen expected to increase or decrease? - The volatility is increasing so yes the risk is increasing.
3. Based on the model evaluation, would you feel confident in using these models for trading? - The ARMA model is not significant based on the (p > 0.05), so it doesn't allow us to do a good judgement call. ARIMA model (p > 0.05) - I would not use it for the estimations as well. GARCH model (p < 0.05) gives us more confidence to predict volatility but it does not allow to make a buy/sell call. I won't be confident in using these models at least in ARMA / ARIMA (p=2 and q=1 / p=5, d=1, q=1).

Linear Regression Forecasting notebook completes the following:

1. Data Preparation (Creating Returns and Lagged Returns and splitting the data into training and testing data)
2. Fitting a Linear Regression Model.
3. Making predictions using the testing data.
4. Out-of-sample performance.
5. In-sample performance.

Findings:

1. Does this model perform better or worse on out-of-sample data compared to in-sample data? - Out-of-Sample Performance Root Mean Square Error (RMSE): 0.41545437184712763 is lower than In-of-Sample Performance Root Mean Square Error (RMSE): 0.5962037920929946 so Out-of-Sample data are more significant

References:

1. https://online.stat.psu.edu/stat510/lesson/11/11.1
2. https://scikit-learn.org/stable/modules/linear_model.html
3. http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm