I have recently entered the N.Ireland housing market and have been taking a keen interest in its prospects. Being a ‘number hugger’ I decided to look a little closer at the house sales data supplied by the UK National Statistics Office to assess if the market is really on the road to recovery after the 2007-2009 financial crisis and its unprecedented effect on the N.Ireland housing market. I decided to attempt to predict where the market will go in the next few years using some commonly using statistical forecasting techniques. As asset prices are notoriously difficult to predict I will look at the market depth (proxied by number of monthly transactions over £40K) as a indicator of the market’s recovery and build a statistically optimal forecasting model.

To assess this I use a monthly training data set over the period jan2008-dec2014. I use the exponential smoothing modelling technique, a widely used forecasting technique in statistics. This technique is a weighted average of past observations that allows for forecasts to include the patterns in previous observations and can account for the additive or multiplicative nature of the seasonal, trend and noise components of a financial time series ^{1}

The plots below shows the monthly total house sales in Northern Ireland over the Jan 2008- Sept 2013 period (red line), fitted values from the ETS models (blue line), and forecasts over the Jan 2015- Jan 2017 period (blue line). The forecasts were produced using a Rob Hyndman’s excellent exponential smoothing package in R^{2}. Figure 1 shows a statistically optimal model, while Figure 2 shows a sub optimal model (where a multiplicative trend has been added) which has an upward trend in the forecasts. Both models have a multiplicative seasonal term and confidence intervals are calculated using a normal approximation.

Firstly both model show a strong seasonal trend in the market depth which is exactly what you would expect; its harder to sell your house in winter. Interestingly, even though visually there seems to be a trend upwards in recent months, the optimising algorithm does not identify any trend term in the optimal model. When I force the model to trend upwards in Figure 2 the forecasts are more visually appealing but the width of 95% confidence intervals suggest that these forecasts are vastly more inaccurate. ^{3}

The optimal model (Figure 1) suggests a stabilised seasonal trend going forward but given the larger confidence intervals as we move into the future this forecast is far from accurate.

My analysis on forecasting NI house sales is far from exhaustive but I can draw some general conclusions. Overall while the market has now stabilised in recent years, there are few signs of a sustained recovery in terms of the number of housing being sold above £40K. It will be many years (if ever) before we will return to the irrational exuberance of house buying we seen in the lead up to the 2007-2008 crash. Personally I hope such a market never returns.

## FIGURE 1: Optimal Model using Hyndman et al 2002 algorithm

## FIGURE 2: A suboptimal model with a multiplicative trend added

Click here for the R Code to recreate this plot.

- See Rob Hyndman’s excellent introductory chapter on the topic ↩
- This package is based on Hyndman’s book on exponential smoothing and uses a statistically optimising algorithm to identify the appropriate model given the training dataset. ↩
- For details of the modelling procedure see:
Hyndman, R.J., Koehler, A.B., Snyder, R.D., and Grose, S. (2002) “A state space framework for automatic forecasting using exponential smoothing methods”,

*International J. Forecasting*,**18**(3), 439–454.Hyndman, R.J., Akram, Md., and Archibald, B. (2008) “The admissible parameter space for exponential smoothing models”.

*Annals of Statistical Mathematics*,**60**(2), 407–426. ↩