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Model Explanations.txt
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Model Explanations.txt
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Model Explainations to be used by Bamise in main project comments/explanations:
1. Auto Arima:
This is a type of ARIMA model that automatically chooses the most optimal values for the parameters like
p: the order of auto-regeression,
d: the order of integration,
and q: the order of moving average.
Auto arima works by performing differencing tests(Canova-Hansen method of finding optimal order of seasonal differencing is used.).
It moves through all combinations of p, q, d in a given range and selects the fit with the least value for a chosen metric.
Metrics commonly used are Kwiatkowski–Phillips–Schmidt–Shin, Augmented Dickey-Fuller, or Phillips–Perron.
We have chosen to use ADF metric for our time series analysis.
We have use auto arima to save time while building and tuning our model since
it would be tedious to select optimal p, q, d values for all 300+ currency pairs in our dataset.
The end result is a better fitted model and more accurate prdeictions for our forecasting project.
Summary plots:
The residual errors appear to have a uniform variance and fluctuate around a mean of zero.
The density plot on the top right suggests a normal distribution with a mean of zero.
The red line is aligned with all of the dots. Any significant deviations would indicate a skewed distribution.
The residual errors are not autocorrelated. Any autocorrelation would imply that the residual errors have a pattern that isn’t explained by the model.
2. Arima:
An ARIMA model is created by using pmdarima module.
The order parameter expects a tuple of three integers representing the number of autoregressive (p), differencing (d), and moving average (q)
terms to include in the model.
These parameters are extracted from the auto-arima model in the previous step by using the order() function.
The model information, coefficient estimates, model diagnostics, Information criteria and residuals are printed using the fitted summary function.
The forecast() method is used to generate a forecast for the next n time periods in the time series using the fitted ARIMA model.
n is the number of test records.
To evaluate the fitting by ARIMA, we have used the below metrics:
1. Mean Squared Error (MSE): MSE measures the average squared difference between the predicted and actual
values of a time series. A lower MSE value indicates better performance. The formula for MSE is:
MSE = (1/n) * Σ(actual_i - predicted_i)^2
where n is the number of observations in the time series, actual_i is the actual value of the i-th observation,
and predicted_i is the predicted value of the i-th observation.
2. Root Mean Squared Error (RMSE): RMSE is the square root of the MSE, and it measures the average distance
between the predicted and actual values of a time series. Like MSE, a lower RMSE value indicates better performance.
The formula for RMSE is:
RMSE = sqrt((1/n) * Σ(actual_i - predicted_i)^2)
3. Mean Absolute Error (MAE): MAE measures the average absolute difference between the predicted and
actual values of a time series. It is less sensitive to outliers than MSE and RMSE. The formula for MAE is:
MAE = (1/n) * Σ|actual_i - predicted_i|
4. Mean Absolute Percentage Error (MAPE): MAPE measures the average percentage difference between the predicted and
actual values of a time series. It is often used to evaluate the accuracy of forecasting models. The formula for MAPE is:
MAPE = (1/n) * Σ|(actual_i - predicted_i)/actual_i|
These metrics are commonly used to evaluate the performance of ARIMA models.
3. FBProphet:
The second model we have tried is the open source prophet model provided by Facebook.
The seasonality mode parameter controls how seasonality is modeled in the time series data. We have chosen additive
by assuming seasonal effects are additive to the trend component.
The parameter daily_seasonality is a boolean that is set to True to include a daily
seasonality component, which means that patterns that repeat on a daily basis will be captured.
Similarly weekly_seasonality is also set to true to capture any weekly seasonaloitys that might be present.
The training data is used to fit the prophet model and it contains a "ds" column which is the
datetime column that represents the time periods in the time series and a "y" column representing the close prices.
The make_future_dataframe() is used to create a new dataframe for future time periods. this is a build in method of the prophet model.
periods parameter specifies the number of time periods for which you want to make predictions. In this case, periods=len(test_data) means
that the number of future time periods is equal to the length of the test data. freq='W-SUN' means that the time series has a weekly
frequency and the week ends on Sunday.
After creating the Prophet model instance and fitting it to the training data, we used it to make predictions for the future time
periods having the length of the test data
using the model.predict() function. The output of the predict() function is a pandas DataFrame that contains the predicted values,
along with the uncertainty intervals for each prediction. The yhat column of the predictions is then used to measure the performance metrics of the model,.
We have use the below metrics to evaluate the prophet model fitting:
1.Mean Squared Error (MSE)
2.Root Mean Squared Error (RMSE)
3.Mean Absolute Error (MAE)
4.Mean Absolute Percentage Error (MAPE)