Introduction 11 involved with acquisitions, will rely more on their knowledge of the local- ity and building to make a buy or sell decision. This has also given rise to so-called ‘judgemental’ forecasts. Real estate markets have gone through severe cycles not predicted by bottom-up analysis, however, and thus this approach to forecasting has been questioned. For many, the winning for- mula is now not just having good judgement about the future direction of the market, but also making a careful quantitative analysis explaining cyclical movements and the impact of broader trends. Therefore, consistent with evidence from other fields, a view that has increasingly gained popular- ity is that the optimal approach arises from a combination of judgemental and quantitative forecasting. Moreover, there is a more generic econometric and forecasting interest. Do quantitative techniques underperform judge- mental approaches or is the combination of quantitative and judgemental forecasts the most successful formula in the real estate market? The book addresses this issue directly, and the tools presented will give the reader a framework to assess such quandaries. Real estate forecasting can also be used for model selection. There are often competing theories available and it may be the case that there is more than one theory-consistent model that passes all the diagnostics tests set by the researcher. The past relative forecasting success of these models will guide model selection for future forecast production and other uses. Finally, forecasting is the natural progression in real estate as more data become available for a larger number of markets. In scholarly activity, the issue of data availability is highlighted constantly. One would expect that, with more data and markets, interest in real estate forecasting will continue to grow. The key objectives of forecasting in real estate are presented in box 1.1. Box 1.1 Objectives of forecasting work (1) Point forecasts. The forecaster is seeking the actual forecast value for rent growth or capital growth in one, two, three quarters or years, etc. (2) Direc tion forecasts. The forecaster is interested in the direction of the forecast and whether the trend is upward or downward (and perhaps an assessment can be made as to how steep this trend will be). (3) Turning point forecasts. The aim in this kind of forecast is to identify turning points or the possibility of a turning point. (4) Confidence. The modelling and forecasting process is used to attach a confidence interval to the forecast, how it can vary and with what probability. (5) Scenario analysis. This is the sensitivity of the forecast to the drivers of the model. The content of this book is more geared to help the reader to perform tasks one, two and five. 12 Real Estate Modelling and Forecasting 1.8 Econometrics in real estate, finance and economics: similarities and differences The tools that we use when econometrics is applied to real estate are funda- mentally the same as those in economic and financial applications. The sets of issues and problems that are likely to be encountered when analysing data are different, however. To an extent, real estate data are similar to economic data (e.g. gross domestic product [GDP], employment) in terms of their frequency, accuracy, seasonality and other properties. On the other hand, there are some important differences in how the data are generated. Real estate data can be generated through the valuation process rather than through surveys or government accounts, as is the case for economic data. There are some apparent differences with financial data, given their high frequency. A commonality with financial data, however, is that most real estate data are not subject to subsequent revisions, or, at least, not to the extent of economic data. In economics, a serious problem is often a lack of data to hand for testing the theory or hypothesis of interest; this is often called a small samples prob- lem. Such data may be annual and their method of estimation may have changed at some point in the past. For example, if the methods used to measure economic quantities changed twenty years ago then only twenty annual observations at most are usefully available. There is a similar prob- lem in real estate markets. Here, though, the problem concerns not only changing methods of calculation but also the point at which the data were first collected. In the United Kingdom, data can be found back to 1966 or earlier, but only at the national level. Databases such as the United King- dom’s Investment Property Databank (IPD) and that of the United States’ National Council of Real Estate Investment Fiduciaries (NCREIF) go back to the 1970s. In other regions, such as the Asia-Pacific retail markets, however, data are available only for about ten years. In general, the frequency dif- fers by country, with monthly data very limited and available only in some locations. As in finance, real estate data can come in many shapes and forms. Rents and prices that are recorded are usually the product of valuations that have been criticised as being excessively smooth and slow to adjust to changing market conditions. The problem arises from infrequent trading and trying to establish values where the size of the market is small. The industry has recognised this issue, and we see an increasing compilation of transactions data. We outlined in section 1.5 above that other real estate market data, such as absorption (a measure of demand), are constructed based on other market information. These data are subject to measurement error and revi- sions (e.g. absorption data are subject to stock and vacancy rate revisions Introduction 13 unless they are observed). In general, measurement error affects most real estate series; data revisions can be less serious in the real estate context compared with economics, however. Financial data are often considered ‘noisy’, which means that it is diffi- cult to separate underlying trends or patterns from random and uninteresting features. Noise exists in real estate data as well, despite their smoothness, and sometimes it is transmitted from the financial markets. We would con- sider real estate data noisier than economic data. In addition, financial data are almost always not normally distributed in spite of the fact that most techniques in econometrics assume that they are. In real estate, normality is not always established and does differ by the frequency of the data. The above features need to be considered in the model-building process, even if they are not directly of interest to the researcher. What should also be noted is that these issues are acknowledged by real estate researchers, valuers and investment analysts, so the model-building process is not hap- pening in a vacuum or with ignorance of these data problems. 1.9 Econometric packages for modelling real estate data As the title suggests, this section contains descriptions of various computer packages that may be employed to estimate econometric models. The num- ber of available packages is large, and, over time, all packages have improved in the breadth of the techniques they offer, and they have also converged in terms of what is available in each package. Some readers may already be familiar with the use of one or more packages, and, if this is the case, this section may be skipped. For those who do not know how to use any econometrics software, or have not yet found a package that suits their requirements – read on. 1.9.1 What packages are available? Although this list is by no means exhaustive, a set of widely used packages is given in table 1.1. The programmes can usefully be categorised according to whether they are fully interactive (menu-driven), command-driven (so that the user has to write mini-programmes) or somewhere in between. Menu- driven packages, which are usually based on a standard Microsoft Windows graphical user interface, are almost certainly the easiest for novices to get started with, for they require little knowledge of the structure of the pack- age, and the menus can usually be negotiated simply. EViews is a package that falls into this category. On the other hand, some such packages are often the least flexible, since the menus of available options are fixed by the developers, and hence, if one 14 Real Estate Modelling and Forecasting Table 1.1 Econometric software packages for modelling financial data Package software supplier EViews QMS Software Gauss Aptech Systems LIMDEP Econometric Software Matlab The MathWorks RATS Estima SAS SAS Institute Shazam Northwest Econometrics Splus Insightful Corporation SPSS SPSS Stata StataCorp TSP TSP International Note: Full contact details for all software suppliers can be found in the appendix at the end of this chapter. wishes to build something slightly more complex or just different, one is forced to consider alternatives. EViews has a command-based programming language as well as a click-and-point interface, however, so it offers flexibility as well as user-friendliness. 1.9.2 Choosing a package Choosing an econometric software package is an increasingly difficult task as the packages become more powerful but at the same time more homoge- neous. For example, LIMDEP, a package originally developed for the analysis of a certain class of cross-sectional data, has many useful features for mod- elling financial time series. Moreover, many packages developed for time series analysis, such as TSP (‘Time Series Processor’), can also now be used for cross-sectional or panel data. Of course, this choice may be made for you if your institution offers or supports only one or two of the above possibilities. Otherwise, sensible questions to ask yourself are as follows. ● Is the package suitable for your intended applications – for example, does the software have the capability for the models that you want to estimate? Can it handle sufficiently large databases? ● Is the package user-friendly? ● Is it fast? ● How much does it cost? Introduction 15 ● Is it accurate? ● Is the package discussed or supported in a standard textbook? ● Does the package have readable and comprehensive manuals? Is help available online? ● Does the package come with free technical support so that you can e-mail the developers with queries? A great deal of useful information can be obtained most easily from the web pages of the software developers. Additionally, many journals (includ- ing the Journal of Applied Econometrics,theEconomic Journal,theInternational Journal of Forecasting and the American Statistician) publish software reviews that seek to evaluate and compare the packages’ usefulness for a given pur- pose. Three reviews that the first author has been involved with are Brooks (1997) and Brooks, Burke and Persand (2001, 2003). 1.10 Outline of the remainder of this book Chapter 2 This chapter aims to illustrate data transformation and computation, which are key to the construction of real estate series. The chapter also provides the mathematical foundations that are important for the computation of statistical tests in the following chapters. It begins by looking at how to index a single data series and produce a composite index from several series by different methods. The chapter continues by showing how to convert nominal data into real terms. The discussion explains why we log data and reminds the reader of the properties of logs. The calculation of simple and continuously compounded returns follows, a topic of much relevance in the construction of real estate series such as capital value (or price) and total returns. The last section of the chapter is devoted to matrix alge- bra. Key aspects of matrices are presented for the reader to help his/her understanding of the econometric concepts employed in the following chapters. Chapter 3 This begins with a description of the types of data that may be available for the econometric analysis of real estate markets and explains the concepts of time series, cross-sectional and panel data. The discussion extends to the properties of cardinal, ordinal and nominal numbers. This chapter covers important statistical properties of data: measures of central tendency, such as the median and the arithmetic and geometric means; measures of spread, 16 Real Estate Modelling and Forecasting including range, quartiles, variance, standard deviation, semi-standard deviation and the coefficient of variation; higher moments – that is, skew- ness and kurtosis; and normal and skewed distributions. The reader is fur- ther introduced to the concepts of covariance and correlation and the metric of a correlation coefficient. This chapter also reviews probability distribu- tions and hypothesis testing. It familiarises the reader with the t- and normal distributions and shows how to carry out hypothesis tests using the test of significance and confidence interval approaches. The chapter finishes by highlighting the implications of small samples and sampling error, trends in the data and spurious associations, structural breaks and data that do not follow the normal distribution. These data characteristics are crucially important to real estate analysis. Chapter 4 This chapter introduces the classical linear regression model (CLRM). This is the first of four chapters we devote to regression models. The material brought into this chapter is developed and expanded upon in subsequent chapters. The chapter provides the general form of a single regression model and discusses the role of the disturbance term. The method of least squares is discussed in detail and the reader is familiarised with the derivation of the residual sum of squares, the regression coefficients and their standard errors. The discussion continues with the assumptions concerning distur- bance terms in the CLRM and the properties of the least squares estimator. The chapter provides guidance to conduct tests of significance for variables in the regression model. Chapter 5 Chapter 5 develops and extends the material of chapter 4 to multiple regres- sion analysis. The coefficient estimates in multiple regression are discussed and derived. This chapter also presents measures of goodness of fit. It intro- duces the concept of non-nested hypotheses and provides a first view on model selection. In this chapter, the reader is presented with the F -test and its relationship to the t-test. With examples, it is illustrated how to run the F -test and determine the number of restrictions when running this test. The F -test is subsequently used in this chapter to assess whether a statistically significant variable is omitted from the regression model or a non-significant variable is included. Chapter 6 This focuses on violations of the assumptions of the CLRM. The discussion provides the causes of these violations and highlights the implications for Introduction 17 the robustness of the models. It shows the reader how to conduct diagnostic checks and interpret the results. With detailed examples, the concepts of heteroscedasticity, residual autocorrelation, non-normality of the residuals, functional form and multicollinearity are examined in detail. Within the context of these themes, the role of lagged terms in a regression is studied. The exposition of diagnostic checks continues with the presentation of parameter stability tests, and examples are given. The chapter finishes by critically reviewing two key approaches to model building. Chapter 7 This chapter is devoted to two examples of regression analysis: a time series specification and a cross-sectional model. The aim is to illustrate further practical issues in building a model. The time series model is a rent growth model. This section begins by considering the data transformations required to address autocorrelation and trends in the data. Correlation analysis then informs the specification of a general model, which becomes specific by applying a number of tests. The diagnostics studied in the previous chapter are applied to two competing models of rent growth to illustrate compar- isons. The second example of the chapter has a focus on international yields and seeks to identify cross-sectional effects on yields. This part of the chapter shows that the principles that are applied to build and assess a time series model can extend to a cross-sectional regression model. Chapter 8 This presents an introduction to pure time series models. The chapter begins with a presentation of the features of some standard models of stochastic processes (white noise, moving average (MA), autoregressive (AR) and mixed ARMA processes). It shows how the appropriate model can be chosen for a set of actual data with emphasis on selecting the order of the ARMA model. The most common information criteria are discussed, which can, of course, be used to select terms in regression analysis as well. Forecasting from ARMA models is illustrated with a practical application to cap rates. The issue of seasonality in real estate data is also treated in the context of ARMA model estimation and forecasting. Chapter 9 This chapter is wholly devoted to the assessment of forecast accuracy and educates the reader about the process of and tests for assessing forecasts. It presents key contemporary approaches adopted for forecast evaluation, including mean error measures, measures based on the mean squared error and Theil’s metrics. The material in this chapter goes further to cover the 18 Real Estate Modelling and Forecasting principles of forecast efficiency and encompassing. It also examines more complete tools for forecast evaluation, such as the evaluation of rolling forecasts. Detailed examples are given throughout to help the application of the suite of tests proposed in this chapter. The chapter also reviews studies that show how forecast evaluation has been applied in the real estate field. Chapter 10 Chapter 10 moves the analysis from regression models to more general forms of modelling, in which the segments of the real estate market are simultaneously modelled and estimated. These multivariate, multi- equation models are motivated by way of explanation of the possible exis- tence of bidirectional causality in real estate relationships, and the simulta- neous equations bias that results if this is ignored. The reader is familiarised with identification testing and the estimation of simultaneous models. The chapter makes the distinction between recursive and simultaneous mod- els. Exhaustive examples help the reader to absorb the concept of multi- equation models. The analysis finally goes a step further to show how fore- casts are obtained from these models. Chapter 11 This chapter relaxes the intrinsic restrictions of simultaneous equations models and focuses on vector autoregressive (VAR) models, which have become quite popular in the empirical literature. The chapter focuses on how such models are estimated and how restrictions are imposed and tested. The interpretation of VARs is explained by way of joint tests of restric- tions, causality tests, impulse responses and variance decompositions. The application of Granger causality tests is illustrated within the VAR con- text. Again, the last part of the chapter is devoted to a detailed example of obtaining forecasts from VARs for a REIT (real estate investment trust) series. Chapter 12 The first section of the chapter discusses the concepts of stationarity, types of non-stationarity and unit root processes. It presents several procedures for unit root tests. The concept of and tests for cointegration, and the formula- tion of error correction models, are then studied within both the univariate framework of Engle–Granger and the multivariate framework of Johansen. Practical examples to illustrate these frameworks are given in the context of an office market and tests for cointegration between international REIT markets. These frameworks are also used to generate forecasts. Introduction 19 Chapter 13 Having reviewed frameworks for simple and more complex modelling in the real estate field and the process of obtaining forecasts from these frame- works in the previous chapters, the focus now turns to how this knowledge is applied in practice. The chapter begins with a review on how forecasting takes place in real estate in practice and highlights that intervention occurs to bring in judgement. It explains the reasons for such intervention and how the intervention operates, and brings to the reader’s attention issues with judgemental forecasting. The reader benefits from the discussion on how judgement and model-based forecasts can be combined and how the relative contributions can be assessed. Ways to combine model-based with judgemental forecasts are critically presented. Finally, tips are given on how to make both intervention and the forecast process more acceptable to the end user. Chapter 14 This summarises the book and concludes. Some recent developments in the field, which are not covered elsewhere in the book, are also mentioned. Some tentative suggestions for possible growth areas in the modelling of real estate series are also given in this short chapter. Key concepts The key terms to be able to define and explain from this chapter are ● real estate econometrics ● model building ● occupier market ● investment market ● development market ● take-up ● net absorption ● stock ● physical construction ● new orders ● vacancy ● prime and average rent ● effective rent ● income return ● initial yield ● equivalent yield ● capital growth ● total returns ● quantitative models ● qualitative models ● point forecasts ● direction forecasts ● turning point forecasts ● scenario analysis ● data smoothness ● small samples problem ● econometric software packages Appendix: Econometric software package suppliers Package Contact information EViews QMS Software, 4521 Campus Drive, Suite 336, Irvine, CA 92612–2621, United States. Tel: (+1) 949 856 3368; Fax: (+1) 949 856 2044; Web: www.eviews.com. Gauss Aptech Systems Inc, PO Box 250, Black Diamond, WA 98010, United States. Tel: (+1) 425 432 7855; Fax: (+1) 425 432 7832; Web: www.aptech.com. LIMDEP Econometric Software, 15 Gloria Place, Plainview, NY 11803, United States. Tel: (+1) 516 938 5254; Fax: (+1) 516 938 2441; Web: www.limdep.com. Matlab The MathWorks Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, United States. Tel: (+1) 508 647 7000; Fax: (+1) 508 647 7001; Web: www.mathworks.com. RATS Estima, 1560 Sherman Avenue, Evanson, IL 60201, United States. Tel: (+1) 847 864 8772; Fax: (+1) 847 864 6221; Web: www.estima.com. SAS SAS Institute, 100 Campus Drive, Cary, NC 27513–2414, United States. Tel: (+1) 919 677 8000; Fax: (+1) 919 677 4444; Web: www.sas.com. Shazam Northwest Econometrics Ltd, 277 Arbutus Reach, Gibsons, BC V0N 1V8, Canada. Tel: (+1) 604 608 5511; Fax: (+1) 707 317 5364; Web: shazam.econ.ubc.ca. Splus Insightful Corporation, 1700 Westlake Avenue North, Suite 500, Seattle, WA 98109–3044, United States. Tel: (+1) 206 283 8802; Fax: (+1) 206 283 8691; Web: www.splus.com. SPSS SPSS Inc, 233 S. Wacker Drive, 11th Floor, Chicago, IL 60606–6307, United States. Tel: (+1) 312 651 3000; Fax: (+1) 312 651 3668; Web: www.spss.com. Stata StataCorp, 4905 Lakeway Drive, College Station, Texas 77845, United States. Tel: (+1) 800 782 8272; Fax: (+1) 979 696 4601; Web: www.stata.com. TSP TSP International, PO Box 61015 Station A, Palo Alto, CA 94306, United States. Tel: (+1) 650 326 1927; Fax: (+1) 650 328 4163; Web: www.tspintl.com. 20 [...]... serious, and they have led to the development of what is known as the Fisher ideal price index, which is simply the geometric mean of the Laspeyres and Paasche approaches 24 Real Estate Modelling and Forecasting The following example illustrates how an index can be constructed using the various approaches The data were obtained from tables 581 and 584 of the web pages of the Department for Communities and. ..2 Mathematical building blocks for real estate analysis Learning outcomes In this chapter, you will learn how to ● construct price indices; ● compare nominal and real series and convert one to the other; ● use logarithms and work with matrices; and ● construct simple and continuously compounded returns from asset prices 2.1 Introduction This chapter... are 30 Real Estate Modelling and Forecasting often used A more detailed discussion as to the most relevant general price index to use is beyond the scope of this book, but suffice to say that, if the researcher is interested only in viewing a broad picture of the real prices rather than a highly accurate one, the choice of deflator will be of little importance The real price series is obtained by taking... 1991 The values for the nominal and real indices in, say, 2005 are calculated as 71.4 = (626/877) × 100 and 60.6 = (6.2/10.2) × 100, respectively For the real rent index, we use column (v) for real rents, but an identical result would be obtained if we used columns (iii) or (vi) A comparison of real and nominal rents is given in figure 2.1 Interestingly, office rents in real terms in Singapore recovered... conducted by first estimating the value of the portfolio at each time period and then determining the returns from the aggregate portfolio values 34 Real Estate Modelling and Forecasting Box 2.3 Two advantages of log returns (1) Log-returns have the nice property that they can be interpreted as continuously compounded returns – so that the frequency of compounding of the return does not matter, and thus... of dispersion, of skewness and of kurtosis for a given series; ● calculate measures of association between series; ● test hypotheses about the mean of a series by calculating test statistics and forming confidence intervals; ● interpret p-values; and ● discuss the most common pitfalls that can occur in the analysis of real estate data 3.1 Types of data for quantitative real estate analysis There are... series data 41 42 Real Estate Modelling and Forecasting Box 3.1 Time series data in real estate Series Rents Yields Absorption Frequency Monthly, quarterly or annually Monthly, quarterly or annually Quarterly or annually It is also generally a requirement that all data used in a model be of the same frequency of observation So, for example, regressions that seek to estimate absorption (demand) using annual... in 2007 prices (this is our last observation, and converting rents into today’s prices Real estate analysis: mathematical building blocks 31 Table 2.7 Construction of a real rent index for offices in Singapore (i) Rent nominal1 (ii) CPI 1991 = 100 (iii) Rent real1 (iv) CPI 2004 = 100 (v) Rent real (vi) Rent 2007 prices1 (vii) (viii) Rents index2 nominal real 1991 1992 1993 1994 877 720 628 699 100.0... matrix by the identity matrix of the appropriate 36 Real Estate Modelling and Forecasting size results in the original matrix being left unchanged: e.g MI = I M = M ● In order to perform operations with matrices (e.g addition, subtraction or multiplication), the matrices concerned must be conformable The dimensions of matrices required for them to be conformable depend on the operation ● The addition and. .. as a short rank matrix, and such a matrix is also termed singular Three important results concerning the rank of a matrix are: rank (A) = rank (A ) rank (A B) ≤ min(rank (A), rank(B)) rank (A A) = rank(A A ) = rank (A) 38 Real Estate Modelling and Forecasting −1 ● The inverse of a matrix A, denoted A , where defined, is that matrix which, when pre-multiplied or post-multiplied by A, will result in the . 3 41, 8 41 350,679 3 81, 713 413 , 412 Haringey 10 1,9 71 106,539 12 4 ,10 6 14 1,050 17 1,660 19 3,083 224,232 236,324 259,604 274,5 31 Islington 12 3,425 14 6,684 17 1,474 206,023 249,636 263,086 290, 018 294 ,16 3. 11 8.77 12 6 .10 13 7.03 14 5.04 Current-weighted 51. 20 60.02 69.56 79.55 10 0.00 10 7.66 11 9.23 12 6.95 13 7.75 14 5.20 Fischer ideal 51. 00 59.96 69.58 79.52 10 0.00 10 7.54 11 9.00 12 6.53 13 7.39 14 5 .12 which. methods 19 96 19 97 19 98 19 99 2000 20 01 2002 2003 2004 2005 Equally weighted 49.73 60.09 71. 39 79.67 10 0.00 10 5. 51 114 .93 12 2.85 13 2 .15 13 9.79 Base-weighted 50.79 59.89 69.59 79.48 10 0.00 10 7. 41 118 .77