Forecasting Future Real Estate Prices using Time Series Analysis

Here, we will explain the procedure for predicting future real estate prices using the ARIMA model.

1. Introduction

In Japan, there are several time series data available as indexes for real estate prices, such as official land prices and standard land prices. When conducting market analysis surrounding real estate, it is common to utilize these indexes. However, there is no specific established method for predicting future price movements, and it tends to rely on the subjective judgment.

In this article, we introduce the basic process of using the ARIMA model, a statistical analysis method for time series data, as an example of a forecasting technique for real estate prices.

2. What is the ARIMA Model?

The ARIMA model is a model that applies the autoregressive model (AR model) and moving average model (MA model) to differenced data. The AR model represents a stochastic process where the model output at time t depends on the model output at previous times, while the MA model represents a stochastic process where the model output at time t depends on the previous error terms. The ARMA model is a model that combines the AR model and MA model to represent a stochastic process.

AR, MA, ARMA model equations:

[Note] c: constant term, φ: autoregressive coefficient, ε: error term, μ: constant term, θ: moving average coefficient

However, while this model has high explanatory power when the analyzed time series data exhibits stationarity, in general, many time series data, including real estate price movements, do not exhibit stationarity.

Note: Stationary data are relatively easier to predict future values and are easier to handle in statistical analysis. On the other hand, non-stationary data have changing means and variances over time, requiring caution in future forecasting and statistical analysis.

In the ARIMA model, non-stationary time series data can be transformed into stationary data by taking the difference of the data. The difference represents the change in the data over time and allows for maintaining a constant level of variability. In the ARIMA model, after transforming the data into stationary form, the autoregressive and moving average models are combined to perform future predictions.

ARIMA model equation:

Additionally, the ARIMA model can be applied to various time series data for future forecasting, including items such as sales revenue and visitor forecasts, as well as methods for calculating inventory increases in national economic calculations.

In Japan, the use of long-term time series data related to real estate is possible due to the system of official land prices. Therefore, as a reference, we provide a basic future forecast using the data. In this article, we have created the program using the R language, widely used for statistical data analysis.

3. Explanation of Analysis Steps and Programming Code

To perform future price prediction using the ARIMA model, we will apply the ARIMA model to the national average land price data from 1975 to 2023, following the steps below:

[Steps]

1. Load the time series data for analysis.
2. Import the necessary libraries for time series analysis.
3. Convert the data format into an analyzable type.
4. Determine whether the time series data is stationary or non-stationary (ADF Test: Augmented Dickey-Fuller test).
5. Determine the appropriate order in the ARIMA model (AIC: Akaike Information Criterion).
6. Apply the determined order to the model and finalize the model.
7. Perform future forecasting using the model.

• ADF Test: A statistical test to determine whether the time series data is a unit root process (a process with a long-term trend and non-stationary characteristics).
• ** AIC: A statistical criterion used to compare the predictive accuracy of different statistical models. It considers the trade-off between the complexity of the model and its predictive accuracy to select the best forecasting model. In this analysis, ARIMA(2,1,0) was determined as the best model based on AIC, so it is adopted in the analysis.

[R Programming Code]

4. Analysis Results and Summary

The analysis results obtained from executing the provided programming code are as follows. The points displayed represent the predicted movements for the next three years starting from 2024.

It should be noted that this analysis is a basic one focusing solely on the time series data, and it does not consider various factors that influence real estate, such as population, number of households, interest rate trends, and economic fluctuations. Therefore, by incorporating these external variables and conducting further analysis, it becomes possible to achieve more advanced future forecasting.

Forecasting the future, including real estate prices, is a highly challenging task. However, applying statistical analysis methods such as the ARIMA model and its variations, and deepening one's understanding and interpretation, can be valuable in conducting real estate price analysis.

Moreover, at Deloitte Tohmatsu, we have a team of experts specializing in real estate and statistical analysis who can provide support for such analyses.