# House Price Forecasting from Investment Perspectives

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Base for Modeling

_{t}is the dividend or cash flow at time t and R is the discount rate. E denotes the expected value.

## 3. Econometric Tools for Model Development

_{0}is a constant, μ is the error correction term, E is a vector of key micro and macroeconomic variables such as population, employment, immigration, bank lending, construction activities, etc. (see Table 1 for exact variables used in Equation (5)), S is a vector for seasonal dummies, and ε is white noise.

## 4. Variable Selection and Description

- (1)
- Australian Bureau of Statistics (ABS). This includes, for example, time-series data on regional population and immigration growth, nationwide bank mortgage lending, building construction cost, and price changes in other capital cities
- (2)
- Securities Industry Research Center of Asia-Pacific (SIRCA). This includes, for example, time-series data on median prices and rents for houses and units in the Greater Sydney Area. We assume that the mix and quality of quarterly residential property sales for houses and units (i.e., the number of bedrooms, bathrooms, car parks, lot size, land tenure, a mix of high- and low-value properties, and transaction types, etc.) are relatively stable over time. The impact of forced sales on reported median price indices as discussed in Renigier-Biłozor, Walacik, Źróbek, and d’Amato [29] is small in this study.
- (3)
- DataStream. This includes, for example, market data on Australia’s interest rates and government bond yields
- (4)
- NSW Planning & Environment. This includes, for example, time-series data related to local housing and land supply.

## 5. Model Development and Testing Results

#### 5.1. Model Development

#### 5.2. Out-of-Sample Testing, Underlying Variable Assumptions, and Measures of Forecasting Accuracy

#### 5.3. Forecasting Results

#### 5.4. Robustness Check

#### 5.4.1. Unconditional Forecast

#### 5.4.2. Forecasted Median Rents

#### 5.4.3. Forecasted Interest Rates

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

(1) | (2) | |
---|---|---|

House Price Changes | Unit Price Changes | |

CointEq1 | −0.084 *** | −0.074 ** |

(0.025) | (0.030) | |

D(LOG(SYD_HP_MEDIAN(-1))) | 0.577 *** | 0.674 *** |

(0.090) | (0.105) | |

D(LOG(SYD_RENT(-1))) | 0.104 | −0.016 |

(0.148) | (0.057) | |

D(LOG(AUS_INT_90D(-1))) | 0.039 | −0.008 |

(0.033) | (0.021) | |

Constant | −0.003 | 0.000 |

(0.005) | (0.004) | |

D(LOG(AUS_INT_10YRF)) | −0.017 | −0.015 |

(0.028) | (0.019) | |

D(LOG(AUS_LEN_DF)) | −0.006 | −0.002 |

(0.043) | (0.029) | |

D(LOG(AUS_CONF)) | −0.143 | −0.073 |

(0.3540) | (0.278) | |

D(LOG(NSW_PPGF)) | −0.006 | |

(0.005) | ||

D(LOG(SYD_SUP_DF)) | 0.011 | −0.000 |

(0.012) | (0.009) | |

D(LOG(SYD_NOMF)) | 0.072 | 0.076 ** |

(0.045) | (0.033) | |

ECC_PCF | 0.001 * | 0.000 |

(0.000) | (0.000) | |

Seasonal dummy | Yes | Yes |

Adj. R-squared | 0.827 | 0.806 |

Sum sq. resids | 0.002 | 0.001 |

S.E. equation | 0.010 | 0.007 |

F-statistic | 14.650 | 11.954 |

Log likelihood | 131.030 | 146.459 |

Akaike AIC | −6.16 | −6.919 |

Schwarz SC | −5.556 | −6.272 |

Mean dependent | 0.008 | 0.009 |

S.D. dependent | 0.023 | 0.015 |

The cointegration equation results | ||

LOG(SYD_HP_MEDIAN_H(-1)) | 1.000 | 1.000 |

LOG(SYD_RENT_H(-1)) | −0.373 (0.202) * | −0.550 (0.079) *** |

LOG(AUS_INT_90D(-1)) | 0.427 (0.102) *** | 0.280 (0.042) *** |

Constant | −11.588 | −10.113 |

## Appendix B

Models | obs. | RMSE | MAE | MAPE | Theil |
---|---|---|---|---|---|

Panel A: Houses | |||||

AR(1) | 20 | 84,743 | 74,407 | 8.179 | 0.051 |

ECM without economic variables | 20 | 91,834 | 78,256 | 9.626 | 0.055 |

Panel B: Units | |||||

AR(1) | 20 | 27,524 | 22,353 | 3.256 | 0.021 |

ECM without economic variables | 20 | 46,490 | 39,064 | 6.140 | 0.036 |

## Appendix C

## Appendix D

## Notes

1 | A time series process with a unit root (a random walk). |

2 | The statistical area of the Greater Sydney Area is maintained by the Australian Bureau of Statistics. For 35 LGAs and their geographic locations and boundaries, please go to the Australian Bureau of Statistics website at: https://dbr.abs.gov.au/index.html (accessed on 25 July 2021). |

3 | The authors went through a wide range of data collection in this study. As not all variables are available or statistically significant in our model, we only report the key variables used in the ECM model, as shown in Table 1. Please contact the corresponding author for a complete list of variables collected in this study. |

4 | Results of Johansen’s cointegration test are available on request from the corresponding author. |

5 | Results are available on request by contacting the corresponding author. |

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Variable | Definition | Sources |
---|---|---|

SYD_HP_MEDIAN_H | Median house prices in the Greater Sydney Area | SIRCA |

SYD_RENT_H | Median house rents in the Greater Sydney Area | SIRCA |

SYD_HP_MEDIAN_U | Median unit prices in the Greater Sydney Area | SIRCA |

SYD_RENT_U | Median unit rents in the Greater Sydney Area | SIRCA |

AUS_INT_90D | Australia 90-day bill rate | Datastream |

AUS_INT_10YRF | Australian ten-year government bond yield | Datastream |

AUS_LEN_DF | Bank mortgage lending for all dwelling finance in Australia | ABS |

AUS_CONF | Building construction cost index of Australia | ABS |

NSW_PPGF | New South Wales population growth | ABS |

SYD_SUP_DF | Total number of dwelling (all types) supply in the Greater Sydney Area | NSW Planning & Environment |

SYD_NOMF | Net migration numbers in the Greater Sydney Area | ABS |

ECC_PCF | Residential Property Price Index percentage change from the corresponding quarter of the previous year-weighted average of eight capital cities | ABS |

Variable Transformation | ||

D(LOG(SYD_HP_MEDIAN_H)) | Changes in median house prices | |

D(LOG(SYD_RENT_H)) | Changes in median house rents | |

D(LOG(SYD_HP_MEDIAN_U)) | Changes in median unit prices | |

D(LOG(SYD_RENT_U)) | Changes in median unit rents | |

D(LOG(AUS_LEN_DF)) | Growth rate of bank mortgage lending | |

D(LOG(AUS_CONF)) | Changes in building construction costs | |

D(LOG(NSW_PPGF)) | Changes in population growth | |

D(LOG(SYD_NOMF)) | Changes in net migration numbers |

(1) | (2) | |
---|---|---|

House Price Changes | Unit Price Changes | |

CointEq1 | −0.048 *** | −0.046 *** |

(0.014) | (0.015) | |

D(LOG(SYD_HP_MEDIAN(-1))) | 0.536 *** | 0.639 *** |

(0.071) | (0.076) | |

D(LOG(SYD_RENT(-1))) | 0.009 | −0.007 |

(0.107) | (0.054) | |

D(LOG(AUS_INT_90D(-1))) | 0.017 | −0.007 |

(0.021) | (0.014) | |

Constant | −0.002 | −0.000 |

(0.003) | (0.003) | |

D(LOG(AUS_INT_10YRF)) | −0.003 | −0.001 |

(0.015) | (0.011) | |

D(LOG(AUS_LEN_DF)) | 0.007 | 0.011 |

(0.034) | (0.025) | |

D(LOG(AUS_CONF)) | −0.291 | −0.210 |

(0.269) | (0.215) | |

D(LOG(NSW_PPGF)) | −0.003 | |

(0.004) | ||

D(LOG(SYD_SUP_DF)) | 0.003 | −0.006 |

(0.008) | (0.007) | |

D(LOG(SYD_NOMF)) | 0.042 | 0.052 * |

(0.036) | (0.028) | |

ECC_PCF | 0.002 *** | 0.001 *** |

(0.000) | (0.000) | |

Seasonal dummy | Yes | Yes |

Adj. R-squared | 0.843 | 0.812 |

Sum sq. resids | 0.003 | 0.006 |

S.E. equation | 0.009 | 0.012 |

F-statistic | 24.567 | 2.966 |

Log likelihood | 200.977 | 184.466 |

Akaike AIC | −6.447 | −5.878 |

Schwarz SC | −5.95 | −5.38 |

Mean dependent | 0.012 | 0.008 |

S.D. dependent | 0.022 | 0.014 |

The cointegration equation results | ||

LOG(SYD_HP_MEDIAN_H(-1)) | 1.000 | 1.000 |

LOG(SYD_RENT_H(-1)) | −0.262 (0.249) | −0.500 (0.117) |

LOG(AUS_INT_90D(-1)) | 0.582 (0.077) *** | 0.412 (0.043) *** |

Constant | −12.475 | −10.609 |

Variable | obs. | RMSE | MAE | MAPE | Theil |
---|---|---|---|---|---|

Panel A: Actual | |||||

Median house prices | 20 | 22,578 | 19,003 | 2.207 | 0.013 |

Median unit prices | 20 | 31,923 | 23,047 | 3.141 | 0.024 |

Panel B: Statistical models | |||||

ARIMA model | |||||

Median house prices | 20 | 53,771 | 45,449 | 5.368 | 0.032 |

Median unit prices | 20 | 24,593 | 20,107 | 2.299 | 0.014 |

AR(1) model | |||||

Median house prices | 20 | 59,000 | 49,203 | 5.776 | 0.035 |

Median unit prices | 20 | 18,484 | 14,111 | 2.068 | 0.014 |

AR(4) model | |||||

Median house prices | 20 | 70,685 | 59,990 | 7.172 | 0.042 |

Median unit prices | 20 | 21,640 | 18,154 | 2.729 | 0.016 |

AR(8) model | |||||

Median house prices | 20 | 64,694 | 54,936 | 6.534 | 0.038 |

Median unit prices | 20 | 21,370 | 18,047 | 2.688 | 0.016 |

AR(16) model | |||||

Median house prices | 20 | 46,217 | 39,780 | 4.712 | 0.027 |

Median unit prices | 20 | 25,551 | 19,379 | 2.836 | 0.019 |

AR(20) model | |||||

Median house prices | 20 | 37,305 | 31,007 | 3.677 | 0.022 |

Median unit prices | 20 | 30,753 | 23,981 | 3.397 | 0.023 |

Houses | Units | |||||
---|---|---|---|---|---|---|

Time Period | ARIMA | AR(1) | AR(20) | ARIMA | AR(1) | AR(20) |

2019Q1 | 931,067 | 935,696 | 930,709 | 708,278 | 711,058 | 707,385 |

2019Q2 | 911,194 | 919,994 | 910,228 | 703,633 | 709,259 | 702,693 |

2019Q3 | 899,668 | 910,522 | 898,726 | 701,262 | 709,549 | 701,167 |

2019Q4 | 899,592 | 902,946 | 898,575 | 704,042 | 709,965 | 705,222 |

2020Q1 | 911,688 | 897,870 | 910,480 | 710,599 | 709,785 | 712,396 |

2020Q2 | 937,604 | 896,699 | 935,054 | 725,269 | 712,940 | 727,899 |

2020Q3 | 969,586 | 898,580 | 963,080 | 742,813 | 717,425 | 744,982 |

2020Q4 | 1,000,454 | 899,203 | 988,440 | 761,172 | 721,061 | 762,201 |

2021Q1 | 1,026,564 | 899,777 | 1,010,434 | 776,647 | 723,352 | 776,808 |

2021Q2 | 1,051,763 | 902,546 | 1,035,673 | 793,422 | 728,505 | 794,303 |

2021Q3 | 1,072,154 | 907,377 | 1,061,955 | 807,664 | 734,725 | 810,899 |

2021Q4 | 1,084,812 | 910,416 | 1,085,048 | 818,901 | 739,903 | 827,012 |

2022Q1 | 1,090,764 | 913,157 | 1,103,916 | 825,515 | 743,606 | 838,728 |

2022Q2 | 1,097,922 | 918,003 | 1,122,849 | 833,694 | 750,172 | 852,274 |

2022Q3 | 1,104,906 | 924,863 | 1,141,454 | 841,290 | 757,768 | 864,616 |

2022Q4 | 1,110,291 | 929,794 | 1,158,450 | 848,505 | 764,205 | 877,111 |

2023Q1 | 1,115,409 | 934,287 | 1,176,081 | 854,240 | 769,020 | 887,132 |

2023Q2 | 1,127,265 | 940,781 | 1,201,009 | 864,403 | 776,693 | 902,642 |

2023Q3 | 1,143,098 | 949,182 | 1,229,239 | 876,219 | 785,338 | 919,601 |

2023Q4 | 1,159,630 | 955,449 | 1,255,977 | 888,902 | 792,691 | 937,265 |

2024Q1 | 1,176,506 | 961,117 | 1,280,240 | 900,605 | 798,278 | 951,949 |

2024Q2 | 1,199,588 | 968,711 | 1,307,132 | 916,464 | 806,760 | 970,516 |

2024Q3 | 1,224,766 | 978,157 | 1,329,884 | 933,008 | 816,191 | 986,871 |

2024Q4 | 1,247,488 | 985,306 | 1,341,254 | 948,795 | 824,226 | 999,107 |

2025Q1 | 1,267,094 | 991,752 | 1,340,653 | 961,684 | 830,379 | 1,003,737 |

2025Q2 | 1,289,900 | 1,000,113 | 1,336,449 | 977,148 | 839,503 | 1,009,010 |

2025Q3 | 1,311,892 | 1,010,324 | 1,330,797 | 991,885 | 849,581 | 1,011,236 |

2025Q4 | 1,328,916 | 1,018,109 | 1,324,326 | 1,004,629 | 858,177 | 1,012,546 |

2026Q1 | 1,341,300 | 1,025,120 | 1,321,241 | 1,013,773 | 864,786 | 1,012,437 |

2026Q2 | 1,356,635 | 1,034,069 | 1,329,277 | 1,025,616 | 874,466 | 1,019,592 |

2026Q3 | 1,371,711 | 1,044,895 | 1,343,665 | 1,037,221 | 885,119 | 1,029,243 |

2026Q4 | 1,382,851 | 1,053,181 | 1,359,345 | 1,047,595 | 894,211 | 1,040,725 |

2027Q1 | 1,390,980 | 1,060,639 | 1,374,828 | 1,055,374 | 901,217 | 1,050,439 |

2027Q2 | 1,404,237 | 1,070,076 | 1,396,359 | 1,067,094 | 911,409 | 1,066,013 |

2027Q3 | 1,419,395 | 1,081,436 | 1,420,529 | 1,079,755 | 922,604 | 1,082,358 |

2027Q4 | 1,432,427 | 1,090,149 | 1,441,346 | 1,092,156 | 932,161 | 1,098,464 |

2028Q1 | 1,444,141 | 1,097,988 | 1,459,068 | 1,102,630 | 939,534 | 1,110,928 |

2028Q2 | 1,462,484 | 1,107,862 | 1,480,598 | 1,117,673 | 950,221 | 1,128,060 |

2028Q3 | 1,483,687 | 1,119,714 | 1,503,627 | 1,133,929 | 961,946 | 1,144,919 |

2028Q4 | 1,503,083 | 1,128,815 | 1,524,299 | 1,149,803 | 971,957 | 1,161,090 |

2029Q1 | 1,521,148 | 1,137,001 | 1,544,480 | 1,163,369 | 979,686 | 1,174,553 |

2029Q2 | 1,545,758 | 1,147,287 | 1,572,678 | 1,181,283 | 990,865 | 1,194,720 |

2029Q3 | 1,572,689 | 1,159,614 | 1,606,490 | 1,199,862 | 1,003,123 | 1,216,369 |

2029Q4 | 1,596,568 | 1,169,086 | 1,640,703 | 1,217,315 | 1,013,591 | 1,238,525 |

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## Share and Cite

**MDPI and ACS Style**

Shi, S.; Mangioni, V.; Ge, X.J.; Herath, S.; Rabhi, F.; Ouysse, R.
House Price Forecasting from Investment Perspectives. *Land* **2021**, *10*, 1009.
https://doi.org/10.3390/land10101009

**AMA Style**

Shi S, Mangioni V, Ge XJ, Herath S, Rabhi F, Ouysse R.
House Price Forecasting from Investment Perspectives. *Land*. 2021; 10(10):1009.
https://doi.org/10.3390/land10101009

**Chicago/Turabian Style**

Shi, Song, Vince Mangioni, Xin Janet Ge, Shanaka Herath, Fethi Rabhi, and Rachida Ouysse.
2021. "House Price Forecasting from Investment Perspectives" *Land* 10, no. 10: 1009.
https://doi.org/10.3390/land10101009