Welcome back. This week, we are continuing with Business forecasting for when our time series data exhibits a seasonal component. Decomposition is an alternative method for analyzing and predicting time series that explicitly states how the components of the time series interact to produce the observed series. Decomposition also allows us to remove just the seasonal component from the raw data and deseasonalized it, or remove just the trend component from the raw data and de-trend it. Decomposition is an alternative to the Winter's method when seasonal and trend components are present. The explicit model for decomposition is of the form displayed on your screen, where Y_ t is a function of seasonality, trend, a cycle, and a random component. The form of the function will be determined by the time series. The seasonal component should be one where the fluctuations due to seasonality are constant over all season cycles. Just as for winters, we can have a multiplicative decomposition or an additive decomposition. In the Excel, ScreenFlow videos, we will focus on multiplicative decomposition, as it is the more general case. If you want to look at additive decomposition, you can have a look at the resources in this week's toolbox. There are seven steps to a forecasting using decomposition. Removing the seasonality and random fluctuations from the raw data using a centered moving average, by getting the average for a window that is as long as a year. Calculating seasonal relatives by dividing each observation by the centered moving average, which is a proxy for the yearly average. Averaging all seasonal relatives of the same period for each of the years to generate seasonal indices. De-seasonalizing the data by dividing it by the relevant seasonal index. Identifying the trend component T in the de-seasonalized time series via a trend equation, which is usually linear. Using this trend equation to generate the trend line estimates. Forecasting using the trend line estimates and the seasonal indices. Forecasting with the decomposition model is really a re-composition of the projected values of the systematic components. We take the estimated values from the trend equation and multiply the seasonal index back in. Beyond forecasting as a bonus, we can also de-trend the data by taking the raw data and removing the trend that we just estimated. As you can probably gather, there seems to be a bit of mechanics here. But with practice, you will realize that it is quite intuitive because you will see the business meaning behind every calculation we perform in each step. The added advantage of the decomposition method is that you gain extra business intelligence by being able to observe the de-seasonalized data with the seasonal fluctuations removed and the de-trended data with the trend component removed. When your data, says "sales figures are fluctuating" you can get a better picture of the underlying sales figures to gain that extra bit of business intelligence for decision making, strategy, and forward planning. Rather than just looking at the raw figures alone, will then end the week by looking at a statistical tool called a Correlogram. Correlograms have two uses in business forecasting. One, it can help us check whether our errors are random and that we have truly captured all the components in our forecasting model. Two, before we even begin to model, if the systematic components of our time series are not that obvious, even after plotting a line chart, a correlogram may help us in identifying the systematic components. A correlogram visually represents a statistical concept known as an auto correlation function, which is an estimate of how a certain value in a series is correlated with past or lagged values of that series. The horizontal x-axis represents time, the number of lags, and the vertical y-axis represents the auto-correlation function, or ACF. The lower and upper confidence intervals are bounds. They are to judge statistical significance or not. Beyond either of the bounds, an ACF is statistically significant, within the bounds, an ACF is not statistically significant. Now, depending on the Excel add-in that you use, you may get an ACF for a lag of zero, which is not so helpful as the ACF for a lag of zero will be one. The data point is perfectly correlated to itself. We will be deleting any ACF for a lag of zero for all our analysis. The correlogram for a raw data series with only a random component should look like this. All the ACFs are within the bounds. Thus, after constructing any time-series business forecasting model, it is good practice to plot the correlogram of the errors to ensure that our errors are truly random. Thus, our model has captured all the relevant components. The correlogram for a series with a trending component, either an upward trend or a downward trend, will have the ACFs slowly decreasing over time. The correlogram for a series with a seasonal component, will have the ACFs going out of either of the bounds at lags, which are related to the periodicity of the data. The fourth and/or eighth lag for quarterly data, for example. The correlogram for a series with the level component will have a spike in the ACF out of one of the bounds for the very first leg and then the subsequent ACFs will be within the bounds. Unfortunately, because of the nature of the cyclical component, which has periodicity that is not regular, a correlogram cannot help us here. Judgment is needed for the cyclical component. It is somewhat subjective, but there are useful methods that are used in business for this. We will be focusing on judgmental forecasting in our third course of this specialization, Excel skills for business forecasting, judgmental forecast. By the end of this week, you'll have finished this course. Everyone say, wow. Reflect on what you've learned, how far you've come and how you can apply this to your own work setting. Apart from the quizzes and discussion board you've had each week, this week, you have an assessment that draws upon the entire course on time series forecasting methods. You'll actually have fun with this assessment, which is actually an assessment for your learning as much as it is an assessment of your learning. Once you attain your certificate for this course, make sure you post it on social media and especially LinkedIn to showcase your achievements and build a community of learning and practice for business forecasting. Remember, the journey continues in our second course of this specialization, Excel skills for business forecasting, regression models. Let's get into our last few Excel ScreenFlow videos. Everyone say "wow".
