Arima stock market
This article was first published on R programming , and kindly contributed to R-bloggers. Many of you must have come across this famous quote by Neils Bohr, a Danish physicist.
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Prediction is the theme of this blog post. In this post, we will cover the popular ARIMA forecasting model to predict returns on a stock and demonstrate a step-by-step process of ARIMA modeling using R programming.
Forecasting involves predicting values for a variable using its historical data points or it can also involve predicting the change in one variable given the change in the value of another variable.
Forecasting approaches are primarily categorized into qualitative forecasting and quantitative forecasting. Time series forecasting falls under the category of quantitative forecasting wherein statistical principals and concepts are applied to a given historical data of a variable to forecast the future values of the same variable. Some time series forecasting techniques used include:.
ARIMA stands for Autoregressive Integrated Moving Average. ARIMA is also known as Box-Jenkins approach. Box and Jenkins claimed that non-stationary data can be made stationary by differencing the series, Y t. We will follow the steps enumerated below to build our model. To model a time series with the Box-Jenkins approach, the series has to be stationary. A stationary time series means a time series without trend, one having a constant mean and variance over time, which makes it easy for predicting values.
Testing for stationarity — We test for stationarity using the Augmented Dickey-Fuller unit root test. The p-value resulting from the ADF test has to be less than 0. If the p-value is greater than 0. Differencing — To convert a non-stationary process to a stationary process, we apply the differencing method.
Differencing a time series means finding the differences between consecutive values of a time series data. The differenced values form a new time series dataset which can be tested to uncover new correlations or other interesting statistical properties. We apply the appropriate differencing order d to make a time series stationary before we can proceed to the next step.
In this step, we identify the appropriate order of Autoregressive AR and Moving average MA processes by using the Autocorrelation function ACF and Partial Autocorrelation function PACF. For AR models, the ACF will dampen exponentially and the PACF will be used to identify the order p of the AR model. If we have one significant spike at lag 1 on the PACF, then we have an AR model of the order 1, i. If we have significant spikes at lag 1, 2, and 3 on the PACF, then we have an AR model of the order 3, i.
For MA models, the PACF will dampen exponentially and the ACF plot will be used to identify the order of the MA process.
If we have one significant spike at lag 1 on the ACF, then we have an MA model of the order 1, i. If we have significant spikes at lag 1, 2, and 3 on the ACF, then we have an MA model of the order 3, i.
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Once we have determined the parameters p,d,q we estimate the accuracy of the ARIMA model on a training data set and then use the fitted model to forecast the values of the test data set using a forecasting function.
In the end, we cross check whether our forecasted values are in line with the actual values. Now, let us follow the steps explained to build an ARIMA model in R. There are a number of packages available for time series analysis and forecasting.
We load the relevant R package for time series analysis and pull the stock data from yahoo finance. In the next step, we compute the logarithmic returns of the stock as we want the ARIMA model to forecast the log returns and not the stock price.
We also plot the log return series using the plot function. Next, we call the ADF test on the returns series data to check for stationarity. The p-value of 0. If the series were to be non-stationary, we would have first differenced the returns series to make it stationary. In the next step, we fixed a breakpoint which will be used to split the returns dataset in two parts further down the code.
We truncate the original returns series till the breakpoint, and call the ACF and PACF functions on this truncated series. We can observe these plots and arrive at the Autoregressive AR order and Moving Average MA order.
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We know that for AR models, the ACF will dampen exponentially and the PACF plot will be used to identify the order p of the AR model. For MA models, the PACF will dampen exponentially and the ACF plot will be used to identify the order q of the MA model.
Thus, our ARIMA parameters will be 2,0,2. Our objective is to forecast the entire returns series from breakpoint onwards. We will make use of the For Loop statement in R and within this loop we will forecast returns for each data point from the test dataset.
In the code given below, we first initialize a series which will store the actual returns and another series to store the forecasted returns.
In the For Loop, we first form the training dataset and the test dataset based on the dynamic breakpoint. We call the arima function on the training dataset for which the order specified is 2, 0, 2. We use this fitted model to forecast the next data point by using the forecast.
One can use the confidence level argument to enhance the model. We will be using the forecasted point estimate from the model.
We can use the summary function to confirm the results of the ARIMA model are within acceptable limits. In the last part, we append every forecasted return and the actual return to the forecasted returns series and the actual returns series respectively. Before we move to the last part of the code, let us check the results of the ARIMA model for a sample data point from the test dataset. The standard error is given for the coefficients, and this needs to be within the acceptable limits.
The Akaike information criterion AIC score is a good indicator of the ARIMA model accuracy. Lower the AIC score better the model. We can also view the ACF plot of the residuals; a good ARIMA model will have its autocorrelations below the threshold limit.
The forecasted point return is Let us check the accuracy of the ARIMA model by comparing the forecasted returns versus the actual returns. The last part of the code computes this accuracy information.
If the sign of the forecasted return equals the sign of the actual returns we have assigned it a positive accuracy score. One can try running the model for other possible combinations of p,d,q or instead use the auto. To conclude, in this post we covered the ARIMA model and applied it for forecasting stock price returns using R programming language. We also crossed checked our forecasted results with the actual returns.
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