ARIMA
<h2 id="definition">Definition</h2> <p>ARIMA, standing for AutoRegressive Integrated Moving Average, is a forecasting technique used to analyze and predict future trends in time series data. It's a powerful model in Corporate Performance Management (CPM) for predicting financial and operational metrics essential for strategic planning and decision-making.</p> <p>The ARIMA model combines three components: Autoregressive (AR) - leveraging the relationship between an observation and a number of lagged observations, Integrated (I) - differing the observations to make the time series stationary, and Moving Average (MA) - using the dependency between an observation and a residual error from a moving average model applied to lagged observations. This blend makes ARIMA adaptable for a wide range of time series data, including those with trends and seasonality, providing corporate finance professionals with a robust tool for detailed forecasting.</p> <h2 id="types">Types</h2> <p>Modern forecasting tools in the CPM space have the ability to automatically inspect historical data and suggest a model. It may suggest ARIMA, or SARIMA if sufficient seasonality is present.</p> <table> <thead> <tr> <th><strong>Model</strong></th> <th><strong>Explanation of Its Use</strong></th> </tr> </thead> <tbody> <tr> <td>ARIMA(1,0,0)</td> <td>Models a time series based on its own lagged values. Useful for data showing a slow mean reversion to a long-term average.</td> </tr> <tr> <td>ARIMA(0,1,0)</td> <td>Differencing the series once makes it stationary, suitable for random walk models with no constant trend or seasonality.</td> </tr> <tr> <td>ARIMA(1,1,0)</td> <td>Combines differencing with lagged values, good for data with a trend but without seasonal fluctuations.</td> </tr> <tr> <td>ARIMA(0,1,1)</td> <td>Uses differencing and a moving average model, appropriate for smoothing data with a trend but minimal noise.</td> </tr> <tr> <td>ARIMA(0,2,1)</td> <td>Twice-differenced data with a moving average, for series with a more pronounced trend.</td> </tr> <tr> <td>ARIMA(0,2,2)</td> <td>Similar to ARIMA(0,2,1) but with an additional level of smoothing for erratic data.</td> </tr> <tr> <td>ARIMA(1,1,2)</td> <td>Incorporates autoregression, differencing, and a more complex moving average, suitable for data with a trend and moderate seasonality.</td> </tr> </tbody> </table> <h2 id="suggested-use-case">Suggested Use Case</h2> <table> <thead> <tr> <th><strong>Model</strong></th> <th><strong>Suggested Use Case</strong></th> </tr> </thead> <tbody> <tr> <td>ARIMA(1,0,0)</td> <td>Forecasting sales data where trends revert slowly to a long-term average.</td> </tr> <tr> <td>ARIMA(0,1,0)</td> <td>Modeling stock prices or indices where changes are random over time.</td> </tr> <tr> <td>ARIMA(1,1,0)</td> <td>Predicting economic indicators that gradually evolve over time.</td> </tr> <tr> <td>ARIMA(0,1,1)</td> <td>Analyzing and forecasting retail sales with steady growth patterns.</td> </tr> <tr> <td>ARIMA(0,2,1)</td> <td>Long-term investment analysis where the trend shows acceleration.</td> </tr> <tr> <td>ARIMA(0,2,2)</td> <td>Evaluating real estate price trends that may have abrupt changes.</td> </tr> <tr> <td>ARIMA(1,1,2)</td> <td>Planning inventory for products with predictable seasonality and trend.</td> </tr> </tbody> </table> <h2 id="5-important-considerations">5 Important Considerations</h2> <ol> <li><strong>Data Stationarity:</strong> Verify that the time series data is stationary, meaning it has a consistent mean and variance over time.</li> <li><strong>Model Selection:</strong> Choosing the correct ARIMA model parameters (p, d, q) is essential for the model's effectiveness.</li> <li><strong>Seasonality:</strong> If the data exhibits strong seasonal effects, consider extending the model to SARIMA to account for these patterns.</li> <li><strong>Diagnostic Testing:</strong> Conduct thorough diagnostic tests to validate the model's assumptions and to check the residuals for any patterns.</li> <li><strong>Accuracy Monitoring:</strong> Continuously monitor the forecasting accuracy and be prepared to adjust the model as new data becomes available or conditions change.</li> </ol>