973-723-0423

Over the past couple of years we have used Dynamic Factor Models (DFM) to supplement the forecasting methodologies that have proven to be the most appropriate for hotel market forecasting – curve fitting, exponential smoothing, Box-Jenkins, Bass diffusion, econometric modeling, multiple level forecasting and bootstrapping.

The general purpose of a dynamic factor model is to summarize a large number of related time series into a small number of common factors. The uncovered common factors (often hidden) can be used to help forecast the performance of hotel markets and in many cases improve forecasting of the series.

For example, the models can help us find out how RevPAR has evolved over the years in different markets and whether there have been any predominant common trend lines. Moreover, the models help determine what may have shaped these trend lines, how they may be correlated with performance measures, and where these trend lines may be headed in the future.

Another benefit of using DFM is that we do not require any other (third party) data, apart from the hotel market data. Instead of explaining hotel market variables such as supply, demand, occupancy, ADR or RevPAR using additional macro economic variables such as GDP, employment, real personal income, etc., we use the factor trends returns from the DFM. These factor returns are estimated directly from the historical time-series of data from the hotel markets under study.

Let’s provide a simple example by utilizing monthly RevPAR data for all but three (Detroit, Virginia Beach and St. Louis) of the Top 25 hotel markets in the U.S. for 390 months from January 1987 through June 2019. The markets are all part of the overall U.S. lodging market and none of the markets are isolated from the U.S. macro-economy. The process consists of five steps:

  1. Gather granular non-overlapping hotel market time-series data from the markets under investigation
  2. Log transform and standardize the data
  3. Extract key common trends
  4. Interpret the identified common trends
  5. Generate insights by relating the identified trends to other variables, and,
  6. Project the identified trends to improve existing forecasting models.

All the monthly RevPARs were log-transformed to reduce skewness and then standardized to have a zero mean and a unit standard deviation. Figure 1 presents the resulting 22 time series.

A cursory observation of the graphs below reveals a few notable temporal RevPAR patterns. First, many markets show strong seasonality, with peaks and valleys at regular intervals, but not necessarily sharing the same cycle. Secondly, all the markets show growth, however, there has been little consistency due to the impact of recessions and the cyclical nature of the lodging industry during the 390-month period.

To see through the 22 individual time series and grasp the “big picture,” we need a device that can help identify the common trajectories hidden underneath all the observed data. This is where DMF models have a role.

The models are used to simultaneously analyze a large number of time series to distill them into a few key latent dynamic factors that isolate seasonal cyclic movements from non-seasonal, nonstationary trend lines.

Figure 1: Standardized RevPAR Patterns for the Top 22 Hotel Markets in the U.S. from January 1987 to June 2019

Source: Hotel Investment Strategies, LLC based on STR data.

Our DFA model offers a dynamic dimension reduction tool that allows us to capture as much of the co-movement patterns shared by the 22 hotel markets with as few latent factors as possible. To determine the optimal number of latent factors, we need to balance goodness of fit, parsimony, and interpretability.

We ran about seven DFA models and opted on a four-factor solution. It is well established that more factors isn’t per se better when it comes to forecasting. Estimating many factors defeats the purposes of DFM analysis, which is; Summarizing large quantities of data into a few common factors. The outputs for the one through four factor outputs are illustrated below.

Latent Trends for the One -Through Four Dynamic Factor Models for Monthly RevPAR for 22 Top Hotel Markets 1M1987-6M2019

Source: Hotel Investment Strategies, LLC

It is remarkable that with only one factor illustrated above, the model explained 74.7% of the variance observed across 22 markets over 390 months. This increased to 86.5% for two factors, 91.2% for three factors and 93.2% for four factors.

The second column in Table 1 below reports the percentage of variance explained for each RevPAR time series, with a minimum of 82.3% for New York and a high of 98.8% for Los Angeles. The table presents the estimated factor loadings for each market. The larger the absolute value of the loadings, the stronger the correlation between the market and the latent trend.

Latent Trend 1, with large positive loadings for Boston, Chicago, Washington DC and Philadelphia, could be earmarked as a seasonality model for legacy city hotel markets. Latent Trend 2, with largest loadings for Phoenix, New Orleans, Tampa, Orlando and Miami could be deemed a seasonality trend for southern and leisure based cities with a fundamentally different seasonality structure. Latent Trend 3 appears to represent more of a trend for non legacy cities such as Dallas, Atlanta, Denver and Seattle.

Latent Trend 4 reflects a long term trend with cycles with the largest loadings for Washington DC, New Orleans, New York and Philadelphia. Because the factors are estimated simultaneously, it cannot be said which factor trend is “dominant”. It is important to note that for any given row in the table, it is rarely the case that each observed time series is tied exclusively to a single factor.

Table 1: Latent Factor Loadings and Percentages of Variances Explained by R square

Source: Hotel Investment Strategies, LLC

At this juncture we use one of several forecasting methods to forecast the latent trends for several years. The latent trends and their forecasts are then used in either Autoregressive Distributed Lag (ARDL) or our econometric models to forecast the future RevPAR performance of a market.

Dynamic Factor Models can be used to summarize the information contained in a large number of economic (time) series into a small number of factors common to the original set of (time) series. We apply dynamic factor models to hotel market variables such as supply, demand, occupancy, ADR and RevPAR.

We use forecasts of the estimated factor returns to forecast monthly and quarterly RevPAR along with other hotel market variables. Our results indicate that the forecasts generally improve when the dynamic factors are used. Dynamic factor models constitute an active and a growing area of research, both in econometrics, in macroeconomics and in recent years, real estate, finance and hospitality.