I have used Time Series Analysis to predict the behavior and pattern of Passengers at a bus stop, Data Visualizations include Time-Series Plots.
‘Time’ is the most important factor which ensures success in a business. It’s difficult to keep up with the pace of time. But, technology has developed some powerful methods using which we can ‘see things’ ahead of time. Don’t worry, I am not talking about Time Machine. Let’s be realistic here!
I’m talking about the methods of prediction & forecasting. One such method, which deals with time based data is Time Series Modeling. As the name suggests, it involves working on time (years, days, hours, minutes) based data, to derive hidden insights to make informed decision making.
Time series models are very useful models when you have serially correlated data. Most of business houses work on time series data to analyze sales number for the next year, website traffic, competition position and much more. However, it is also one of the areas, which many analysts do not understand.
So, if you aren’t sure about complete process of time series modeling, this guide would introduce you to various levels of time series modeling and its related techniques.
Let’s begin from basics. This includes stationary series, random walks , Rho Coefficient, Dickey Fuller Test of Stationarity. If these terms are already scaring you, don’t worry – they will become clear in a bit and I bet you will start enjoying the subject as I explain it. Stationary Series There are three basic criterion for a series to be classified as stationary series :
(i). The mean of the series should not be a function of time rather should be a constant. The image below has the left hand graph satisfying the condition whereas the graph in red has a time dependent mean.
(ii). The variance of the series should not a be a function of time. This property is known as homoscedasticity. Following graph depicts what is and what is not a stationary series. (Notice the varying spread of distribution in the right hand graph)
(iii). The covariance of the i th term and the (i + m) th term should not be a function of time. In the following graph, you will notice the spread becomes closer as the time increases. Hence, the covariance is not constant with time for the ‘red series’.
- Differencing : This is the commonly used technique to remove non-stationarity. Here we try to model the differences of the terms and not the actual term. For instance,
x(t) – x(t-1) = ARMA (p , q)
This differencing is called as the Integration part in AR(I)MA. Now, we have three parameters
p : AR d : I q : MA
- Seasonality : Seasonality can easily be incorporated in the ARIMA model directly. More on this has been discussed in the applications part below.
Step 3: Find Optimal Parameters The parameters p,d,q can be found using ACF and PACF plots. An addition to this approach is can be, if both ACF and PACF decreases gradually, it indicates that we need to make the time series stationary and introduce a value to “d”.
Step 4: Build ARIMA Model With the parameters in hand, we can now try to build ARIMA model. The value found in the previous section might be an approximate estimate and we need to explore more (p,d,q) combinations. The one with the lowest BIC and AIC should be our choice. We can also try some models with a seasonal component. Just in case, we notice any seasonality in ACF/PACF plots.
Step 5: Make Predictions Once we have the final ARIMA model, we are now ready to make predictions on the future time points. We can also visualize the trends to cross validate if the model works fine.
Applications of Time Series Model Now, we’ll use the same example that we have used above. Then, using time series, we’ll make future predictions. We recommend you to check out the example before proceeding further.