Stats week 3
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Time Series
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When given data that looks at changes to a variable over an extended period of time, it is important to account for seasonal adjustments that may occur within that time series. To account for the seasonality, it is beneficial to break the data down into or decompose the data into pieces. The first breakdown is into systematic and non-systematic components. There are four components to time series decomposition:
· Level: The average value in the series.
· Trend: The increasing or decreasing value in the series.
· Seasonality: The repeating short-term cycle in the series.
· Noise: The random variation in the series. (Brownlee, 2017)
Since I currently work in the real estate industry and I see that the housing market is very seasonal, it was an obvious choice for me to choose the housing market as an example of decomposition of a time series. The busy months are in the summer with the months before and after tapering off as time moves further away from July. The two main drivers behind the seasonality are the nicer weather and the ease of moving when children are not in school. Conversely, the winter months are extremely slow. The cold weather and parents not wanting to have their children change schools during the school year are big factors. In addition, the busy holiday season adds to the slow market conditions. This creates a very repetitive cycle of peaks and valleys. It is easy to see when graphed over time. The oscillating line that is created indicates that time series decomposition is necessary to account for the change in volume as it aligns with the time of year.
When given a time series, determining between using the additive decomposition method and the multiplicative decomposition method is determined by looking at the consistency of the relationship of the seasonal data as compared to time. The easiest way to identify the relationship to graph the variable on the y-axis overtime on the x-axis. Once graphed analyze the shape of the graph, specifically looking at the peaks and valleys created by the seasonality over the given time period.
Multiplicative Model:
Choose the multiplicative model when the magnitude of the seasonal pattern in the data depends on the magnitude of the data. In other words, the magnitude of the seasonal pattern increases as the data values increase and decrease as the data values decrease. ("Additive models and multiplicative models - Minitab", 2020) A sample of a graph for a multiplicative model is seen below.
Shanna Mckinney
Time Series Decomposition
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A time series is a dataset of values ordered in time. The time can be captured monthly, quarterly, or annually. Time could also be captured by the minute, hour, or daily. “In a time series, time is often the independent variable and the goal is usually to make a forecast for the future.” (Peixeiro 2019) The time series decomposition is another tool that can be used to further analyze the elements captured in the series separately. “The classical time series decomposition assumes that a series of interest comprises of three underlying components which combine to produce the data under investigation. These three components are the trend-cycle, the seasonal component and the irregular component. Typically, these components are denoted as Tt, St and Et respectively, with the series of interest denoted as Yt “ (Cook 2013)
There are two classical decomposition methods, additive and multiplicative
Additive decomposition: Yt = Tt + St + Et
Multiplicative decomposition: Yt = Tt x St x Et
Each element of the time series is then separated or isolated . The isolation of each element allows the analyst to create modifications of the original series which can then be used for forecasting and additional analysis. I believe a good example of time series is the production analysis I complete for my team each month. We capture the monthly activity for the team. Some of the elements we measure each month (this list is not exhaustive) are which member of the team completed each task, the sources used to produce each report and the amount of time each report took to complete. A decomposition of the data series could be used to identify a trend in the data sources. It could also be used to determine if there is a seasonal patterned that could be identified each quarter-end or month-end.
The ability to identify when you should use the additive decomposition method versus multiplicative decomposition method can sometimes present a challenge. It is important to review the data element and analyze the original data graph to help determine the best fit. I believe that an additive decomposition method is most beneficial when variation is constant over time. While a multiplicative decomposition method would be better utilized when variation rises over time. ” An additive model is linear where changes over time are consistently made by the same amount. A linear trend is a straight line. A multiplicative model is nonlinear, such as quadratic or exponential. Changes increase or decrease over time. A nonlinear trend is a curved line. A non-linear seasonality has an increasing or decreasing frequency and/or amplitude over time.” (Brownlee 2019) I believe that the stats I produce for my team is a good example of when additive decomposition could be used. The stats are linear. For the most part the changes are consistent. While quarterly corporate earnings are a good example of when multiplicative decomposition could be used. Earnings do not normally follow any patterns. They typically are nonlinear. Earnings could be affected by many different elements. Those elements could be related to the overall effect of the market or related directly to the business. These elements could cause a swing in earnings one direction or another without following any discernable pattern. Each element in the series can be visualized in Excel using the Data Analysis tool.
Reference
Brownlee, J. (August 28, 2019). How to Decompose Time Series Data into Trend and Seasonality. Retrieved from: https://machinelearningmastery.com/decompose-time-series-data-trend-seasonality/
Cook, S. (April nd, 2013 )Time Series Decomposition: A practical example using a classic data set. Retrieved from: tps://www.economicsnetwork.ac.uk/showcase/cook_timeseries
Peixeiro, M. (February 5, 2019). Almost Everything You Need to Know About Time Series. Retrieved from: https://towardsdatascience.com/almost-everything-you-need-to-know-about-time-series-860241bdc578
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As we can see, the distance or amplitude between the peaks and valleys increases as we move away from the origin. This shows that the relationship is exponential.
Additive Model:
Choose the additive model when the magnitude of the seasonal pattern in the data does not depend on the magnitude of the data. In other words, the magnitude of the seasonal pattern does not change as the series goes up or down. ("Additive models and multiplicative models - Minitab", 2020) A Sample of a graph for an additive model is seen below.
In this example the distance of the peaks and valleys are much more consistent as we move away from the origin.
In both cases, the direction of trend does not play a part in determining the method that should be used even though it is a part of the decomposition of a time series.
Reference
Additive models and multiplicative models - Minitab. (2020). Retrieved 4 March 2020, from https://support.minitab.com/en-us/minitab/19/help-and-how-to/modeling-statistics/time-series/supporting-topics/time-series-models/additive-and-multiplicative-models/
Brownlee, J. (2017). How to Decompose Time Series Data into Trend and Seasonality. Retrieved 4 March 2020, from https://machinelearningmastery.com/decompose-time-series-data-trend-seasonality/#:~:text=Time%20series%20decomposition%20involves%20thinking,time%20series%20analysis%20and%20forecasting .
Evans, J., & Basu, A. (2013). Statistics, data analysis, and decision modeling. Boston: Pearson.
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