Prediction on Land Market Value Based on the Real Estate Market in USA

Email: fiona901587@yahoo.com Abstract: The Land Market Value, defined as the total value of land price and quantity data are derived from data on housing values, is an important factor in the estimation of structure costs using price indexes for housing and construction costs. In this study, we gather and analyze 34 years’ national data on past and present real estate transaction. According to the characteristics of raw data, we try to develop the potential Decomposition, Smoothing, ARIMA and other advanced forecasting models with appropriate transformations. Specifically, we employ an innovation space state underlying certain forecasting model. For regression analysis, we involves GDP, CPI, Construction Cost Index, population, unemployment rate, inflation rate and Purchasing Manage Index in multivariate statistical model. Most importantly, we obtain how to add value to business and apply skills set to real estate in a real world environment. The goal in providing crucial statistical method is to enable government and investors to make informed decisions regarding real estate.


Introduction
This paper aims to provide important information of real estate market in USA and potential problems and opportunities or buyer and seller. As housing is a form of wealth, the purchase of a home represents an important investment and it is normally a hot topic for the scholars and investors. Because of scarcity, the fluctuation of land market value will have a great influence of the net worth of business and household. In this regard, Davis and Heathcote (2007) estimate that wings in residential land prices accounted for most of the variation in house prices over  for the United States as a whole. Davis and Palumbo (2008) reach the same conclusion for a large set of metropolitan areas over a somewhat shorter sample period, as do Bostic et al. (2007) in their detailed analysis of home price changes within a single metropolitan area (Wichita, Kansas). In addition, the land is an important component of wealth. Also, it is a source of variation in real estate prices and as collateral for loans, only a handful of studies have calculated land price indexes for the nation as a whole or for a broad set of cities. Davis and Heathcote (2007) and Davis and Palumbo (2008) estimate price indexes for residential land, while Davis (2009) estimates indexes for both residential and commercial land. Also, Sirmans and Slade (2009) use transaction prices to calculate national land prices indexes. The data were collected on the basis of past and present real estate transactions and develop processes which guide future investment by demonstrating the true future value of the investment. To provide students with sufficient understanding and ability to model, analyze and develop forecasts for engineering and business decisions. The emphasis will be on quantitative methods.

Background
After food and medical care, housing is the largest consumer expenditure in the United states. In 1994, personal consumption expenditures on housing were about $2600 per capita, or 14.9% of household budgets. Further, the bulk of expenditures in one of the next highest categories, household operations, are linked to housing. From the investment side, housing is the largest single form of fixed capital investment in the United States, comprising more than $9 trillion, or roughly half of this nation's gross fixed private capital. Other than human capital, housing and land are more widely held than any other form of capital. In United States, as in most countries, the market for housing services can be approximated as a competitive market. Housing production activities have few barriers to entry or large economies of scale. Few landlords or developers are large enough to exert significant market power. The Table 1 showed the mechanism of housing market.
Housing is the largest asset of most American households, so the housing market profoundly affects the distribution of wealth; housing's location and tenure could well affect the behavior of its occupants. Hence, we work on how housing market works? In a good economic situation when house prices are consistently rising, most consumers can afford what is perceived to be full market value for a given property, because the inherent assumption is that value will continue to rise.

Regression Analysis and Dynamic Regression Models
For regression method, as shown in Fig. 1, we mainly measures how the land market value, in terms of GDP, CPI, construction cost index and unemployment rate, inflation rate, population and purchasing manage index, enables a relationship with the real estate market and investment.
Besides, we explore the quantitative and qualitative relationship among these economic variables at risk scenarios. Firstly, we developed two regression models with raw data and log transformation. After checking all the significance of all explanatory variables and residuals of autocorrelation, we obtain Equation 1 and 2. From the Equation 1, we may simply conclude that the land market value is highly related to IR, UR, CCI and PMI.
Where: Considering the multicollinearity within the multiple regressions, we only dropped the variables which are highly related to other variables in the regression, such as GDP and PP in Equation 1. Because such variables GDP and PP are capturing the effect of other variables. However, unemployment usually indicate more economic distress and lower production which causes lower demand for economic purchases including land. Hence, it shows the negative relation to the Land Market Value. Because of the big sample size, we keep some insignificant variables in our model, the effects of those variables, PMI and UR, are negligible. Also, we get rid of the effects of multicollinearity for the selected variables in Equation The log transformation of the regression model can help stabilize the variance. Hence, we try to fit the log transformed model of Equation 2. The transformed model statistical summary shown below.
However, from the Table 2 and 3, we may conclude that there are some evidence of autocorrelation in the residuals of Equation 1 and 2, it indicates there are some information from the data. Hence, we extended the regression method into the general class of dynamic regression models, which simply combined regression models with ARIMA errors. We take into account several formula as the theoretical foundation: where, n t denotes the errors from the regression models and e t denotes the errors from the ARIMA model. Only the ARIMA model errors are assumed to be white noise. From the plots and non-parametric tests of e t in Fig. 2, we may conclude that the residuals of the AR (2) from the regression model is stationary. Compared to three regression equations, the dynamic method is better than others.

Time Series Decomposition and Smoothing Analysis
For time series decomposition models, we have a couple of options, such as the classical additive decomposition, classical multiplicative decomposition and STL decomposition. The classical decomposition is basic and simple way to forecast the trend. We employ the simple exponential smoothing method, holt's linear method, exponential smoothing method and additive damped method and multiplicative damped method. Eventually, the exponential smoothing model could have better forecasting on the trend in Fig. 3.
For ETS(M,A,N) model, we take this into innovation by considering multiplicative error equations: where the ε ∼NID(0,σ 2 ), l t denotes an estimate of the level of the series at time t, b t denotes an estimate of the trend (slope) of the series at time t, α denotes the smoothing parameter for level. β denotes the smoothing parameter for the trend. By the method of minimizing the "likelihood". We estimate the smoothing parameters α, β, b and l. In our model, the estimated parameters are α = 0.9051, β = 0.9051, l = 836.1576, b = 388.3622. The possible values that the smoothing parameters can take is restricted. Traditionally the parameters have been constrained to lie between 0 and 1 so that the equations can be interpreted as weighted averages. For the state space models, we have set 0< α < β <1.

Time Series Analysis
In the mature economies LMV illustrate the importance of land as a source of wealth, but in rapidly growing economies land has an even more significant role in determining economic welfare and a host of incentives for the performance of the economy. From the time series graph, we may find that the American land market value shows stable increase from 1982 to 2004, but from 2005 this number increased dramatically and peaked in 2006,12.55. In fact, the economic crisis started in 2006 in USA, the economics crisis led to the increased interest, hence, the LMV rose rapidly. However, LMV decreased from 12.55 to 5.54 which is the relative lower level in 2012. The economy of USA experienced the great recession during this period. Until 2013, the situation recovered and this number rose to 7.594 in 2015.
Conflicting results are very common when performing forecasting competitions between methods. As forecasting tasks can vary by many dimensions (length of forecast horizon, size of test set, forecast error measures, frequency of data, etc.), it is unlikely that one method will be better than all others for all forecasting scenarios. What we require from a forecasting method are consistently sensible forecasts and these should be frequently evaluated against the task at hand.
Obviously, in Fig. 4, Land Market Value is an increasing time series dataset. We tried original data and log transformation data to fit the ARIMA model. The Table 4 showed all the potential models. Eventually, the Box-Ljung test of residual met the assumption of the non-parametric, it indicates that autocorrelation come from the white noise, but the Log transformation reduced the RMSE significantly, which is almost near to 0.1. Hence, we selected the Log ARIMA (2,0,1) for forecasting model.

Conclusion and Outlook
As the Fig. 5 indicate that, for the data extending into 2015, Log ARIMA (2,0,1) is the best forecasting model among others. We mainly evaluate forecasting models based on the two performance measures of RMSE and AIC. As was the case with the forecast in Table 5, land market value is projected to continue increase in the following years. It shows the stable increase in the future. This number will significantly rise to 7.3 in 2018.