Forecasting Housing Prices: Model Instability and ...

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Jan 24, 2018 - forecast F at an interval t that we can combine. F is a forecast of a single model: F = w1F1 + w2F2 + w3F3 + ... + wnFn. With: w1 + w2 + w3 + .
Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection Carlo Drago

University of Rome “Niccolo Cusano”

5th Business Systems Laboratory International Symposium Naples 24 January 2018

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Outline

Research problem

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Outline

Research problem Methodology

Outline

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Outline

Research problem Methodology Results

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Outline

Research problem Methodology Results Conclusions and directions for future research

Outline

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Outline

Research problem Methodology Results Conclusions and directions for future research

Outline

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Complexity

The economic system can be considered a complex system. The economic system is characterized by multiple interconnections and multiple relationships between the economic agents. We can think about a not so rational agents and so the network is a typical structure, which can be thought as ubiquitous on various economic situations.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Complexity

The economic system can be considered a complex system. The economic system is characterized by multiple interconnections and multiple relationships between the economic agents. We can think about a not so rational agents and so the network is a typical structure, which can be thought as ubiquitous on various economic situations. For instance: Good markets World trade (Serrano and Bogun´ a 2003) Financial markets (Bonanno et al. 2001) More in general markets can be seen as based on a network structure. See Jackson (2008) Many different schools of the economic thought can be seen on this framework of complexity (see Foster 2005)

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Complexity

The increasing complexity of the financial structures, the interconnections between the different economic agents over time can lead the economic and the economic and the financial system to greater instability.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Complexity

The increasing complexity of the financial structures, the interconnections between the different economic agents over time can lead the economic and the economic and the financial system to greater instability. It is very important to understand the aspects of an econonomic and a financial system which lead to an higher instability.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Complexity

The increasing complexity of the financial structures, the interconnections between the different economic agents over time can lead the economic and the economic and the financial system to greater instability. It is very important to understand the aspects of an econonomic and a financial system which lead to an higher instability. More in particular it is necessary to analyze the interconnectedness of the financial sytems and at the same time the different transmission of the shocks which can occur on these networks (Moghadam and Vinals 2010)

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Complexity

The increasing complexity of the financial structures, the interconnections between the different economic agents over time can lead the economic and the economic and the financial system to greater instability. It is very important to understand the aspects of an econonomic and a financial system which lead to an higher instability. More in particular it is necessary to analyze the interconnectedness of the financial sytems and at the same time the different transmission of the shocks which can occur on these networks (Moghadam and Vinals 2010) In this sense the uncertainty and the heterogeneity of markets on the economic system is a relevant known fact. It is fundamental the way on which the economic agents can react to the information.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Financial Complexity

The Research Problem

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Financial Complexity

The Research Problem

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Complex Market behaviors can be determined by the interaction of different heterogeneous agents. In this sense various agent based models simulate the complex behavior of the financial markets by the interaction of simple rules (Sperka and Spisak 2011 and 2012).

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Complex Market behaviors can be determined by the interaction of different heterogeneous agents. In this sense various agent based models simulate the complex behavior of the financial markets by the interaction of simple rules (Sperka and Spisak 2011 and 2012). Price changes on the markets can depend on the interaction between heterogeneous agents.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Complex Market behaviors can be determined by the interaction of different heterogeneous agents. In this sense various agent based models simulate the complex behavior of the financial markets by the interaction of simple rules (Sperka and Spisak 2011 and 2012). Price changes on the markets can depend on the interaction between heterogeneous agents. These agents are intelligent (or they act intelligently) and their expectations are typically rational (Sperka and Spisak 2013).

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Complex Market behaviors can be determined by the interaction of different heterogeneous agents. In this sense various agent based models simulate the complex behavior of the financial markets by the interaction of simple rules (Sperka and Spisak 2011 and 2012). Price changes on the markets can depend on the interaction between heterogeneous agents. These agents are intelligent (or they act intelligently) and their expectations are typically rational (Sperka and Spisak 2013). Experiments can be performed using agent based moldels (see for example Spisak and Sperk 2014) In this sense complexity can be determined from simple rules. It is important at this point to stress and to focus on the problem of the rationality on the markets.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Complex Market behaviors can be determined by the interaction of different heterogeneous agents. In this sense various agent based models simulate the complex behavior of the financial markets by the interaction of simple rules (Sperka and Spisak 2011 and 2012). Price changes on the markets can depend on the interaction between heterogeneous agents. These agents are intelligent (or they act intelligently) and their expectations are typically rational (Sperka and Spisak 2013). Experiments can be performed using agent based moldels (see for example Spisak and Sperk 2014) In this sense complexity can be determined from simple rules. It is important at this point to stress and to focus on the problem of the rationality on the markets.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Complexity on Financial Markets

Following Brunnermeier and Oehmke 2009 it is important to consider complexity relevant when the agents in financial markets tends to be ”boundedly rational”.

The Research Problem

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Following Brunnermeier and Oehmke 2009 it is important to consider complexity relevant when the agents in financial markets tends to be ”boundedly rational”. The meaning of the expression is that it is necessary in order to understand the concept of complexity going outside the classical model in which agents tend to be perfectly rational.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Complexity on Financial Markets

Following Brunnermeier and Oehmke 2009 it is important to consider complexity relevant when the agents in financial markets tends to be ”boundedly rational”. The meaning of the expression is that it is necessary in order to understand the concept of complexity going outside the classical model in which agents tend to be perfectly rational. in this sense the agents does not receive necessarily an advantage on obtaining the information from the markets. See Brunnermeier and Oehmke (2009). The reaction of the economic agents are difficult to be modelled. Sources of instability of markets On this framework relevant sources of instability of markets are the speculative bubbles.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Instability

A relevant problem is that it is possible from the system directly observe an increase of the financial instability of the system. So in this case we can to discuss about the ”financial instability hypothesis” Minsky (1992).

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Financial Instability

A relevant problem is that it is possible from the system directly observe an increase of the financial instability of the system. So in this case we can to discuss about the ”financial instability hypothesis” Minsky (1992). Financial Instability Hypothesis: (Minsky 1992) Capitalism systems are characterized by different cycles. Agents tend to be ciclically characterized by different level of ”expectation” and ”optimism” to the economic activity. In this sense financial bubbles can be determined by the over-optimism of the economic agents until the bubble disappear. In this sense the system is characterized by the endemic instability.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles

The speculative bubbles are very important in economics but their nature is unclear and they are very difficult to be identified.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles

The speculative bubbles are very important in economics but their nature is unclear and they are very difficult to be identified. Bubbles A speculative bubble is related to a trade on an asset or a good which is outside a range of the real inherent economic value of the asset or good.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles

The speculative bubbles are very important in economics but their nature is unclear and they are very difficult to be identified. Bubbles A speculative bubble is related to a trade on an asset or a good which is outside a range of the real inherent economic value of the asset or good. At the same time: there is no a clear reason in literature on why they appear or disappear over the time. The most known reason is the fact that the speculative bubbles depends on the irrational behaviour of the economic agents and their behaviour produces market instability endogenously.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles

The speculative bubbles are very important in economics but their nature is unclear and they are very difficult to be identified. Bubbles A speculative bubble is related to a trade on an asset or a good which is outside a range of the real inherent economic value of the asset or good. At the same time: there is no a clear reason in literature on why they appear or disappear over the time. The most known reason is the fact that the speculative bubbles depends on the irrational behaviour of the economic agents and their behaviour produces market instability endogenously. There are many different examples on the financial history of speculative bubbles as the Dutch Tulip Mania and at the same time the ”railways manias” in different countries as United Kingdom and United States.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Detecting Speculative Bubbles

The growth of the speculative bubbles In this sense there are markets which shows a higher propensity to the growth of the speculative bubbles and also to the growth of instabilities due to the behaviour of the agents. Rationality in this sense it could be affected by the irrational expectations of the economic agents.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Detecting Speculative Bubbles

The growth of the speculative bubbles In this sense there are markets which shows a higher propensity to the growth of the speculative bubbles and also to the growth of instabilities due to the behaviour of the agents. Rationality in this sense it could be affected by the irrational expectations of the economic agents. Statistical models for the identification In this sense the endemic instability of the economic systems and the irrationality of the agents behaviour need to be carefully considered on the statistical models in order to obtain better predictive results. In this sense it is important to consider also rolling approaches to statistical modelling in order to detect early the early signs of some relevant economic changes which can occur over the time.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles on Housing Markets

These procedures can be useful at the same time to anticipate the speculative bubbles on different markets.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles on Housing Markets

These procedures can be useful at the same time to anticipate the speculative bubbles on different markets. Housing markets Housing markets, for instance, are very instable and they are characterised by specifying speculative bubbles. In this sense the housing is directly linked to other relevant economic phenomena, then it is necessary to take into account the behaviour of the agents over time.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

The Research Problem

Speculative Bubbles on Housing Markets

These procedures can be useful at the same time to anticipate the speculative bubbles on different markets. Housing markets Housing markets, for instance, are very instable and they are characterised by specifying speculative bubbles. In this sense the housing is directly linked to other relevant economic phenomena, then it is necessary to take into account the behaviour of the agents over time. Statistical methods Forecasting house prices it is very relevant for the economic implications of the housing on the economic systems, so their relevance cannot be undervalued. So we consider an approach to detect changes on the time series models of the housing prices.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

S&P/Case-Shiller U.S. National Home Price Index

The Research Problem

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Methodology

Forecasting In this respect we consider and compare different forecasting approaches based on autoregressive neural networks with other methodologies and combinations.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Methodology

Forecasting In this respect we consider and compare different forecasting approaches based on autoregressive neural networks with other methodologies and combinations. Preliminary results show a relevant nonlinear structure of these types of data due to the complexity of the underlying economic phenomena.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Methodology

Forecasting In this respect we consider and compare different forecasting approaches based on autoregressive neural networks with other methodologies and combinations. Preliminary results show a relevant nonlinear structure of these types of data due to the complexity of the underlying economic phenomena. Combinations of different methodologies seems particularly useful to predict complex economic phenomena

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Combining Forecasts in practice

Forecasting process Defining the optimal number of observation to consider. Rolling regressions? Multivariate Forecasting

Methodology

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Combining Forecasts in practice

Forecasting process Defining the optimal number of observation to consider. Rolling regressions? Multivariate Forecasting Model selection Base scenario: considering all methods. Selecting the number of methods to use in the combination.

Methodology

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Seeking the Optimal combination: Models selection

The Hierarchical procedure of the model selection Comparing model performances

Methodology

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Seeking the Optimal combination: Models selection

The Hierarchical procedure of the model selection Comparing model performances Ranking the Forecasting models by one or more criteria

Methodology

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Seeking the Optimal combination: Models selection

The Hierarchical procedure of the model selection Comparing model performances Ranking the Forecasting models by one or more criteria Detecting Structural Breaks.

Methodology

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Seeking the Optimal combination: Models selection

The Hierarchical procedure of the model selection Comparing model performances Ranking the Forecasting models by one or more criteria Detecting Structural Breaks. Varying model selection Dynamic Choice. Diagnostics of the single method, ranking and method variations. Choosing the appropriate combination of forecasting models to taking into account the data structure.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Combination Schemes and Strategies

Combination Schemes So let F is a forecast of a single model. So in all case we have a set of n forecast F at an interval t that we can combine. F is a forecast of a single model: F = w1 F1 + w2 F2 + w3 F3 + ... + wn Fn With: w1 + w2 + w3 + ... + wn = 1 and w (1) ≥ 0, w (2) ≥ 0...w (n) ≥ 0 for all the weights w . Base scenario: w1 = w2 = ....wn = 0 consindering all forecasts Alternative: w1 ...wn = 0 discarding some forecasts F1 ...Fn , using the trimmed mean

p

1 2 n Alternative: Ft+h = Ft+h + Ft+h + ...Ft+h , using the geometric mean. See Andrawis Atiya Shishiny (2010) and Timmermann (2006).

Alternative: using the harmonic mean: Ft+h =

1 2 n nFt+h Ft+h ...Ft+h

F1

t+h

+F 2

t+h

+F n

t+h

Weight determination: w1 ...wn ≥ 0, with: w1 + w2 + w3 + ... + wn = 1

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Weights determination Optimal weighths determination w1 = w2 = ....wn = 0 as simple criteria has the advantage of the simplicity, but clearly different alternatives could be chosen. A second approach can be related to the variance (we report here the case of two weights as example): 1 1 n Ft+h = [Ft+h ]w1 + [Ft+h ]w2 + ... + [Ft+h ]1−w1 +w2 optimal schemes using a search algorithm using the geometric mean

Let two variances σ21 and σ22 σ12 represent the covariance between the two forecasts. In this case, assuming the weights sum is 1 each weight can be obtained by: w1 =

σ22 −σ12 σ21 +σ22 −2σ12

and also w2 = 1 − w1

or also weighting P by MSE (Stock Watson 1999), so we obtain: k

w1h = Pk

j=−k

2 MSEh+j

Pk

MSE 2 h+j j=−k 1 MSEh+j j=−k k k MSE 1 MSE 2 + h+j h+j j=−k j=−k MSE 1 + h+j j=−k k

w2h = P

P

P

and also

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Weighting determination schemes

Weights determination by regression Linear weights parametrization: Granger and Ramanathan Combination (1984) estimate omitting the intercept: yt = β0 F1 + β1F2 + ... + βnFn + ǫt Nonlinear weights parametrization Changing weights over the time

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Hybrid Forecasting

Identification of the components to model Assumption that the series is composed in parts: for example yt = Lt + Nt where Lt is a linear autocorrelation structure and Nt is a non-linear component. Number of components to decompose the series. Identification of the structured parts to decompose the series.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Hybrid Forecasting

Identification of the components to model Assumption that the series is composed in parts: for example yt = Lt + Nt where Lt is a linear autocorrelation structure and Nt is a non-linear component. Number of components to decompose the series. Identification of the structured parts to decompose the series. Identification and implementation of the Hybrid modeling strategy Methods choice, for exampe ARIMA, as in the case of Zhang (2003) and Maia, De Carvalho, Ludermir (2008) to estimate Lt then obtain ˆt and use other methods as for example neural networks to ǫt = yt − L capture the nonlinear structures of the yt . In particular ǫt = f (ǫt−1 , ǫt−2 ...ǫt−3 ) + kt . The single forecast Fn from the model is: ˆt + N ˆt yˆt = L Diagnostics Combination Strategy. Combine F1 ,F2 and so on.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Methodology

In this sense we consider a specific model structure and we predict the prices over time. The approach is based on Exponential Smoothing methods and allow for taking into account also internal structure of the time series considered. We assess and evaluate the different models and specifications in order to detect also a relevant loss to predictive performance due to not expected economic phenomena.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Detecting Instability Finally, in order to detect the model instability at every observation we study the stability of the parameterizations, the predictions and their performance over time. In this way deviations from the initial model can be interpreted and investigated as early signs which can lead to a future more relevant speculative bubble or also economic instability.

Methodology

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Methodology

Methodology

Detecting Instability Finally, in order to detect the model instability at every observation we study the stability of the parameterizations, the predictions and their performance over time. In this way deviations from the initial model can be interpreted and investigated as early signs which can lead to a future more relevant speculative bubble or also economic instability. Forecasts combining and hybrid forecasting When the there is uncertainty on the parameterizations, due for instance to the parameter drift, it is possible to consider an approach based on forecasts combining. The models are also compared with the performance of other hybrid forecasting approaches in which we model also the residuals of the entire model as well.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

Conclusions

Conclusions

Complexity and instability on financial markets can be determined in framework in which agents are characterized by simple rules In this sense the interconnections of the agents and also the imperfect rationality of the agents can determine shocks and also the rise and the burst of speculative bubbles Statistical methods in this sense can be useful to determine and to detect early signs of the speculative bubbles. We have shown an approach to model housing time series and to identify the deviations from a known model

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

References

Reference Bonanno, G., Lillo, F., & Mantegna, R. N. (2001). Levels of complexity in financial markets. Physica A: Statistical Mechanics and its Applications, 299(1), 16-27. Brunnermeier, M., & Oehmke, M. (2009). Complexity in financial markets. Princeton University, 8. Chong, J., & Hurn, A. S. (2016). Testing for speculative bubbles: Revisiting the rolling window. Foster, J. (2005). From simplistic to complex systems in economics. Cambridge Journal of Economics, 29(6), 873-892. Ge, J. (2013, May). Who creates housing bubbles? An agent-based study. In International Workshop on Multi-Agent Systems and Agent-Based Simulation (pp. 143-150). Springer, Berlin, Heidelberg. Goodman, A. C., & Thibodeau, T. G. (2008). Where are the speculative bubbles in US housing markets? Journal of Housing Economics, 17 (2), 117-137. Jones, B. (2014). Identifying speculative bubbles: A two-pillar surveillance framework (No. 14-208). International Monetary Fund.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

References

Reference Hyndman, R. J., & Athanasopoulos, G. (2014). Forecasting: principles and practice. OTexts. 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. Knoll, K., Schularick, M., & Steger, T. (2017). No price like home: global house prices, 1870?2012. The American Economic Review, 107 (2), 331-353. Lind, H. (2009). Price bubbles in housing markets: Concept, theory and indicators. International Journal of Housing Markets and Analysis, 2 (1), 78-90. Jackson M. O. (2008) Social and economic networks. Princeton: Princeton University Press. ISBN 9780691134406. Jagannathan, R., Lamont, O., Pinheiro, M., Rogers, C., Scheinkman, J., & Xiong, W. (2002). Overconfidence and Speculative Bubbles. Minsky, H. P. (1992) The Financial Instability Hypothesis. The Jerome Levy Economics Institute Working Paper No. 74. Available at SSRN: https://ssrn.com/abstract=161024 or http://dx.doi.org/10.2139/ssrn.161024 Moghadam, R., & Vinals, J. (2010). Understanding financial interconnectedness. IMF Policy Paper.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

References

Reference

Serrano, M. A., & Boguná, M. (2003). Topology of the world trade web. Physical Review E, 68(1), 015101. Shiller, R. J. (2015). Irrational exuberance. Princeton university press. Slovik P. (2014) Market Uncertainty and Market Instability in ”Initiatives to address data gaps revealed by the financial crisis”. IFC Bulletin No 34 S&P Dow Jones Indices LLC, S&P/Case-Shiller U.S. National Home Price Index [CSUSHPINSA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CSUSHPINSA, October 28, 2017. Sperka, R., & Spisak, M. (2013). Transaction costs influence on the stability of financial market: agent-based simulation. Journal of Business Economics and Management, 14(sup1), S1-S12.

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Forecasting Housing Prices: Model Instability and Speculative Bubbles Early Detection

References

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