I tested the various time-series tools that I have learned in order to predict future movements in the value of the Japanese yen versus the U.S. dollar.

This task is broken down into two steps:

1. Time Series Forecasting
2. Linear Regression Modeling

In this notebook, I apply time series analysis and modeling to determine whether there is any predictable behavior in Dollar-Yen exchange rate data.

• There is an obvious long-term bullish trend in the Settle price of the historical daily Yen futures data. I see a continuation pattern forming, with price consolidating into a tighter range between 1992 to 2008 forming a symmetrical triangle followed by a price surge and consolidating again in the direction of the trend.

• I decomposed the Settle price into a trend and noise using a Hodrick-Prescott Filter.

• Using futures Settle returns, I estimated an ARMA model with the parameters p=2 and q=1: order=(2, 1).

  • Based on the p-values, the ARMA model is not a good fit because the significance level 𝜶 is .05 (5%) and the p-values are higher (p > 𝜶), therefore the relationship between the variables is not statistically significant and we cannot dismiss the null hypothesis.

• Using the raw Yen Settle Price, I estimated an ARIMA model (order=(5, 1, 1)) and based on the summary results p-values are higher than 0.05 (p > 𝜶), which also indicates that the relationship between the variables are not statistically significant and we cannot dismiss the null hypothesis.

  • The model forecasts the Japanese Yen futures settle price to increase over the 5 day forecast horizon.

• I created a GARCH model to forecast near-term volatility of Japanese Yen futures returns. Based on the summary table, the model seems to be a good fit (p < 𝜶).

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

   Based on this time series analysis, I'm expecting that Yen will appreciate againt the dollar in the long-term. However, considering the near-term volatility of the currency pair and unreliable ARMA and ARIMA forecasts, I would not feel confident in trading short-term. A longer investment time horizon would be a safer decision for now, until I find a more reliable forecasting model.

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

   Near-term volatility of the Japanese Yen futures returns is expected to increase based on the GARCH model, which indicates increasing risk of the Yen and/or a potential financial loss.

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

   The ARMA and ARIMA models are not reliable to use for trading because the p-values are higher than 0.05 (> 0.05) which is not statistically significant and we cannot dismiss the null hypothesis. Therefore, I would not feel confident in basing my trading decisions on just these models.

In this notebook, I built a Scikit-Learn linear regression model to predict Yen futures ("settle") returns with lagged Yen futures returns and categorical calendar seasonal effects.

• Created a series using Returns (Dependent variables) and Lagged Returns (Independent variables) and split the data into training and testing data.
• Fitted a Linear Regression model.
• Made predictions of returns using just the testing data.
• Evaluated the model using out-of-sample data and in-sample data separately.

1. Does this model perform better or worse on out-of-sample data compared to in-sample data?

   The out-of-sample RMSE is lower than the in-sample RMSE. RMSE is typically lower for training data but is higher in this case. Therefore, this model performs better on out-of-sample data compared to in-sample data