Moving Average, Exponential Smoothing and Trend Forecasting

Forecasting is a vital component in business. It predicts future sales in a given company's business given the previous or historical data (Gujarati, 2011). In this context, the study will forecast the sales of electricity for New York City residents from 2001 to 2005 quarterly. The electricity company has been experiencing an increase in customers and bills from 2001-2005. The management wanted to predict the quarterly amount in sales of electricity for the residents for the next year in 2006 to aid in near future decision making. Here, the study will use the previous data on sales of electricity to predict future sales. The study will employ three different methods to predict the number of sales: the moving average, exponential smoothing, and trend forecasting. 

Overview 

Moving Average 

The moving average is a forecasting technique that is used to compute the overall trend in a data set (Zhang et al., 2018). It forecasts the datasets' short-terms trends by adding the recent sales and dividing it by the given periods in the computed average. 

There are two strengths of the moving average. First, the moving average can measure the trend of any given time series data. Secondly, the technique can be employed in both the linear and non-linear trends (Makridakis, Wheelwright & Hyndman, 2008). Lastly, the moving average is simple to understand and compute. 

Limitations 

First, the moving average weighs the data equally hence disregarding how recent and relevant the data is. Secondly, the method ignores data outside the average period, thus does not fully utilize the data (Ghysels and Marcellino, 2018). Lastly, the method provides misleading results with underlying seasonality and forecasting with an unadjusted moving average. 

Table 1 

Model Description
			Model Type
Model ID	Sales	Model_1	ARIMA(4,1,4)(3,0,0)

Table 2 

Model Statistics
Model	Number of Predictors	Model Fit statistics		Ljung-Box Q(18)			Number of Outliers
		Stationary R-squared	R-squared	Statistics	DF	Sig.
Sales-Model_1	0	.547	.965	10.906	7	.143	0

Figure 1 : The Moving average graph 

The moving average approach was used to predict the number of sales expected for the quarters of 2006. From the above analysis, the R-squared is 0.965, which implies that the model explains 96.5% of electricity sales variation. Hence, this is a useful model for predicting electricity sales to residents in the first, second, third, and fourth quarter of 2006. The moving average graph above shows that the predicted or forecasted values for the 1, 2 and 3 quarters will increase and then decrease in the last quarter of 2006. 

Exponential Smoothing 

Exponential smoothing is a technique for forecasting univariate time series data with systematic or seasonal components (Gujarati, 2011). The predictions produced by the exponential smoothening are the weights averages of the past observations, where the weights decay exponentially as the observations get older. 

The strength of exponential smoothing is that it provides more significant predictions based on recent observations. This is because the random variations are neglected; hence it is easier to see the underlying phenomenon (Makridakis, Wheelwright & Hyndman, 2008). Further, the forecasts are more accurate because it accounts for the difference between the actual and projected observations. 

One of the techniques' limitations is that it produces a forecast that lags behind the actual trend (De Livera, Hyndman, and Snyder, 2011). Second, it cannot handle the rend well because it performs forecasts in the short term without seasonal and cyclical variations. 

Table 3 

Model Statistics
Model	Number of Predictors	Model Fit statistics		Ljung-Box Q(18)			Number of Outliers
		Stationary R-squared	R-squared	Statistics	DF	Sig.
Sales-Model_1	0	-.353	.910	13.407	17	.709	0

Figure 2 : Simple Exponential Smoothing 

The simple exponential smoothing approach was used to predict the number of sales expected for the quarters of 2006. From the above analysis, the R-squared is 0.910, which implies that the model explains 91.0% of electricity sales variation. Hence, this is a useful model for predicting electricity sales to residents in years 1, 2, 3, and 4 quarters of 2006. Using the exponential smoothing, the forecasted sales for the 1, 2, and 3 quarters will increase steadily for 2006. 

Trend Forecasting 

Trend forecasting is a technique of performing predictions on time series data based on the past's tangible and concrete numbers (Gujarati, 2011). It works when determining the possible trends based on a given time-series data such as the sales and attempting to extrapolate what will happen in the near future. 

The strength of trend forecasting is measurable and verifiable. Hence it can be replicated, checked, updated, and refined when necessary (Li and Liao, 2017). The limitation of the method is that it is inconsistent. This means that it is difficult to follow the consistent accounting principle when the trend is continuously changing. 

Figure 3 : Trend Forecasting for the electricity sales 

The above is the forecast for the sales of electricity for residents from 2001 to 2005 quarterly. The sales of electricity for quarters 1, 2, 3 and 4 increased in 2006. Therefore, using the trend forecast, the sales of electricity among the residents in 2006 is expected to increase. 

Conclusion 

The purpose of this study was to forecast the sales of electricity for New York City residents from 2001 to 2005, quarterly. Three forecasting techniques were employed, they include, the moving average, exponential smoothing, and trend forecasting techniques. Using the moving average method forecasted that the sales will increase in the first, second and third quarters, and then decrease in the last quarter of 2006. The exponential smoothing forecasted sales will rise steadily for the 1, 2, and 3 quarters of 2006. The trend forecasted that sales of electricity will increase in the 1, 2, 3 and 4 quarters of 2006. Therefore, the three methods forecasted an increase in the electricity sales in 2006. 

References 

Bakar, N.A., and Rosbi, S., 2017. Autoregressive integrated moving average (ARIMA) model for forecasting cryptocurrency exchange rate in high volatility environment: A new insight of bitcoin transaction.  International Journal of Advanced Engineering Research and Science ,  4 (11), pp.237311. 

Booranawong, T., and Booranawong, A., 2017. An exponentially weighted moving average method with designed input data assignments for forecasting lime prices in Thailand.  Jurnal Teknologi ,  79 (6). 

Chaudhuri, D., Mukherjee, M., Khondekar, M.H., and Ghosh, K., 2019. Simple exponential smoothing and its control parameter: A reassessment. In Recent Trends in Signal and Image Processing  (pp. 63-77). Springer, Singapore. 

De Livera, A.M., Hyndman, R.J., and Snyder, R.D., 2011. Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American statistical association ,  106 (496), pp.1513-1527. 

Ghysels, E., and Marcellino, M., 2018.  Applied economic forecasting using time series methods . Oxford University Press. 

Gujarati, D.N., 2011. Econometrics by example. Palgrave MacMillan. 

Makridakis, S., Wheelwright, S.C. and Hyndman, R.J., 2008.  Forecasting methods and applications . John wiley & sons. 

Li, W., and Liao, J., 2017, October. A comparative study on trend forecasting approach for stock price time series. In 2017 11th IEEE International Conference on Anti-counterfeiting, Security, and Identification (ASID)  (pp. 74-78). IEEE. 

Pozzi, F., Di Matteo, T., and Aste, T., 2012. Exponential smoothing weighted correlations.  The European Physical Journal B ,  85 (6), pp.1-21. 

Xie, T., Zhang, G., Liu, H., Liu, F., and Du, P., 2018. A hybrid forecasting method for solar output power based on variational mode decomposition, deep belief networks, and auto-regressive moving average. Applied Sciences ,  8 (10), pp.1901.