Time-series Predictions for NHS Units in the United States

The housing market has experienced various challenges since its last peak in 2005. The immediate drop in house prices in 2007 affected not only the construction industry, but also the entire economy. Since then, compounded challenges such as increased delinquency rates and foreclosures (Bloomberg, 2016). The impact has therefore become widespread up until today. This paper seeks to create a forecast for the future of the housing industry using various forecasting techniques for the purpose of predicting the future of this industry.

Data Patterns for Recent One-Family Houses 

In the first figure, the figure represents sales for one family houses in the US from 1975 to 2011 based on the most recent data for non-seasonally adjusted data. This period is considered sufficient as it captures fluctuations in the market. Normally, the time series will contain the following aspects that are necessary in making the appropriate predictions:

A trend – this is a long term change analysis in the data levels.

Seasonality analysis that enables one to determine the seasons in which the trends are being made.

Cycles – these are fluctuations made in regular patterns based on trends, and

Irregularities, which are random and unexplainable in nature and can be attributed to unforeseen circumstances in the market.

The figure therefore shows that an upward trend, seasonality and cycles are available for the housing data market for one-family houses in 

An auto-correlation function is necessary to measure the correlation between successive observation points between time periods. The k-period plotting enables the researcher to create useful trends between time periods in a bid to get succession between significant points. Figure 2 shows the auto-correlation data for a 12-period for the 1975 to 2012 data, while figure 3 shows the 24-period correlation for the same data (Wilson & Keating, 2007). Figure 2 shows that data, being above the upper limit, is significantly different from zero and keeps decreasing above the upper limit level. Figure 3 shows that the upper limit levels are exceeded by the 12 and 24 time period, confirming that they are significantly different from zero. Therefore, there is seasonality of the data in this case.

Time-series Models Analysis

To get a clearer picture of the trends and seasonality in the NHS data, there were three main time-series models used to get appropriate forecasting: the decomposition model, ARIMA and Winter’s smoothing. Model specification data was used in the case of the data from 1975 and 2011. The data in the last six months (May to November 2011) is the holdout period where the actual data shall be used to determine the accuracy of models as compared to the ex-post forecast. The actual data for this time period shall be used.

For the purpose of estimation and forecasting, Forecast X offered by Microsoft Excel shall be used. A comparison of error measurements, mean absolute percentages (MAPE) and root-mean square error (RMSE) is calculated and displayed in a table in a bid to see how much the original values fit in with the estimates. The MAPE is obtained by dividing the forecast error by the actual value to yield a percentage value. The RMSE is obtained by the square of the forecast error and taking the mean of all squared errors.

Table 1 : MAPE and RMSE

Models	Historical period			Holdout period
	Jan. 1975-April 2011			May 2009-Nov 2011
	MAPE	RMSE	RMSE/Mean*	MAPE	RMSE		RMSE/Mean*
Winter’s exponential smoothing	6.52%	4.62	7.49%	8.13%	2.65	8.54%
Decomposition with exponential smoothing trend	5.30%	3.91	6.35%	6.79%	2.48		8.06%
ARIMA(1,0,0)(2,0,0)	6.98%	4.98	8.17%	8.65%	2.67		9.02%

The most appropriate model to use is the one that has the least error. Therefore, the above data shows that the decomposition model has the smallest RMSE for both the holdout period and that of historical data. As such, this model shall be used for the data from January 1975 to present day (November 2011) to interval forecasts for the subsequent six months between December of 2011 and May 2012 as can be seen in the second table and figure 4 below:

Table 2 : Point and Interval Forecast for End of 2011 and Beginning of 2012

Month	Point forecast	5%	95%
December	27.54	21.26	33.82
January	29.58	23.30	35.85
February	34.24	27.95	40.53
March	35.45	29.17	41.73
April	37.15	30.87	43.43
May	34.78	28.50	41.06

Data Analysis 

When such data is presented in this manner, the main question of consideration is whether the adverse effects that the housing industry had faced are behind it. Therefore, we make use of one tool that could analyze the cyclical factors and predict the outcomes of the industry through an analysis of the turning points of each cycle. As a result, a decomposition model is presented, where cyclical factors from a period of 1995 to November of 2009 (estimate data) and December 2011 to May 2012 in figure 5.

A look at the presentation of cyclical factors does not show any apparent trends or cycles in the data for the NHS sales provided. Therefore, this shows that the time-series component is the only one that can show trends within the data. Nonetheless, the presentation shows that the trough in the trends between 2005 and 2008 has been concluded and the trend is now rising. Recovery is sure for the industry from this show. Furthermore, the trends being predicted in the next six months have shown that it is likely that the recovery trend for the industry is likely to continue over the next six months.

Conclusion 

Based on the conclusions made from this paper, the market has shown that the worst effects that it has felt are now behind it. Therefore, market players can now relax and enjoy the coming days as they prepare for a recovering market in the sale of one-family housing units in the coming days. There is a likely improvement of the market in coming days as the market continues to show an upward trend.

Appendix 

Table 3 : Forecast X Output Table

Forecast -- Decomposition Selected
					Forecast						95% - 5%				95% - 5%
Date			Monthly		Quarterly			Annual			Upper				Lower
Dec-2011			27.54								21.26				33.82
Jan-2012			29.58								23.30				35.85
Feb-2012			34.24								27.95				40.53
Mar-2012			35.45		95.22						29.17				41.73
Apr-2012			37.15								30.87				43.43
May-2012			34.78								28.50				41.06
Accuracy Measures									Value				Forecast Statistics							Value
Mean Absolute Percentage Error (MAPE)									5.28%				Mean							61.03
R-Square									95.86%				Standard Deviation							19.51
Root Mean Square Error									3.96
Method Statistics									Value
Method Selected									Decomposition
Basic Method									Exponential Smoothing
Alpha									1.00
Decomposition Type									Multiplicative

References

Bloomberg. (2016). US New One Family Houses Sold Annual Total MoM SA . Retrieved from Bloomberg Markets: http://www.bloomberg.com/quote/NHSLCHNG:IND

Wilson, H., & Keating, B. (2007). Business Forecasting. New York, NY: McGraw Hill/Irwin.