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My data looks like this: time series of average house prices per day in 100 cities (maybe more) over a two-year period, each with a set of characteristic variables that do not change over time, such as land area, greening rate, latitude, and so on. By training the forecasting model, we hope to predict the housing price in the second year given the characteristic variables and the housing price series in the first year.

Is there a professional term for this kind of data? Can deep learning algorithms such as LSTM and RNN be used to make predictions? If the answer is yes, how should the characteristic variables be incorporated into the model? Thanks a lot!

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From my understanding, your dataset comprises of:

  • A dependent variable in the form of an average house price over two years across 100 cities, i.e. an average house price per city over this period.

  • Independent variables (or characteristic variables as you describe) such as land area, greening rate, latitude, etc.

In this regard, your dataset is not a time series dataset per se. Let us assume that you wanted to predict the average housing price for New York in the second year (as an example).

The only information you have on price is the average housing price across New York for the period in question. If this was a time series prediction problem, you may have a time series with the average daily or monthly price recorded across New York at regular intervals, for instance. There would be multiple observations across the time series that could potentially be used for forecasting purposes, depending on seasonality and trend characteristics of the time series.

As such, a model such as LSTM or RNN would not be appropriate in the absence of this, as these are sequential models that depend significantly on past data to predict future data.

It seems that a linear regression model would be more appropriate, whereby the house price would be calculated based on how the independent variables in the data vary. As a hypothetical example, we might find that a greater land area results in a significant increase in price across New York but not Boston, for instance. Given that the characteristic variables do not change over time, then a linear regression could be of use.

You will need to bear in mind that heteroscedasticity (or an uneven variance across the error terms) are likely to be an issue for the model - as house prices across major cities will likely be more expensive than that of smaller cities. As such, you should ensure that the model is tested and adjusted for heteroscedasticity if necessary.

One potential limitation of this model is likely to be the fact that extraneous variables apart from the characteristics mentioned could impact housing prices and this would not be accounted for in the model. For instance, if interest rates rise over a particular year (as they have been currently doing), then the regression analysis would not take account of this if going on the average price for the previous two years. A time series forecast (in the presence of sufficient data) would also be unlikely to do so, as the impact of rate rises would not be taken into account across historical prices.

Ultimately, my recommended first step is to attempt a linear regression model while screening for multicollinearity and heteroscedasticity, while taking into account that the model may be limited in its predictive power due to the impact of extraneous variables that have not been accounted for in the model.

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  • $\begingroup$ Thanks a lot! However, the house prices series contain the prices in each day, so It means a series contains 365 samples. How do I deal with this type of data then? $\endgroup$
    – Daye Tao
    Commented Jul 20, 2023 at 16:06
  • $\begingroup$ If this is the case, then you could use a time series forecasting model such as ARIMA to predict the house price in its own right - provided the series is suitable for forecasting, i.e. has defined seasonality and trend. $\endgroup$ Commented Jul 20, 2023 at 16:46

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