یک روش گام تصادفی برای پیش بینی نرخ وام مسکن 30 ساله ایالات متحده

Following the implications of term structure theory in an efficient bond market, this study formulates a random walk model that produces unbiased and efficient forecasts of the 30-year mortgage rate for 1987–2006. Forecast accuracy improves with a reduction in lead time but deteriorates with an increase in the forecast horizon. We find, however, no clear trend indicating that forecast accuracy has improved over time. From a more practical perspective, the random walk forecasts of the 30-year mortgage rate and prepayment premium (the spread between 30-year mortgage and 10-year Treasury rates) accurately predict directional change and thus are of value to a user. In exploring the view that the 30-year mortgage rate often moves in tandem with the 10-year Treasury rate, we further find that these rates are cointegrated and thus converge to an equilibrium relation in the long-run.

Coupled with the time invariant term premium assumption, the hypothesis of bond market efficiency suggests that long-term interest rates approximately follow a random walk (Pesando, 1979). A random walk behavior implies that such rates rapidly and fully reflect all relevant information so that future rate changes deviate from zero only in response to unanticipated events. It is widely held that the 30-year home mortgage rate often moves in tandem with the 10-year Treasury rate and is thus expected to exhibit similar stochastic behavior in an efficient market. As the first step in this study, we ask whether the random walk forecasts of the 30-year mortgage rate with varying lead times and forecast horizons are accurate. The answer to this question is important to individuals and businesses in making asset-allocation decisions and to policymakers who closely monitor changes in the interest-rate-sensitive housing market activity for clues about the near-term performance of the economy.1 As shown below, the random walk model generally produces both unbiased and efficient forecasts and accurately predicts the direction of change in the 30-year mortgage rate. Interestingly, existing studies evaluating the survey forecasts of long-term interest rates report unfavorable findings. Friedman (1980), for instance, concludes that the survey forecasts of utility and high-grade municipal bond rates from the biweekly Goldsmith-Nagan Bond and Money Market Letter are not rational. Kolb and Stekler (1996) and Brooks and Gray (2004) show that the survey forecasts of the 30-year US Treasury rate from the Wall Street Journal fail to outperform the naïve random walk forecasts. The study by Baghestani (2006) further reveals that the forecasts of 10-year Treasury and Moody’s Aaa corporate bond rates from the Survey of Professional Forecasters are biased. In light of such survey evidence, we believe the findings of this study are important and merit attention. As the second step in this study, we explore the relation between the rates on 30-year mortgage and 10-year Treasury. These rates are shown to be cointegrated and thus converge to an equilibrium relation in the long-run. Additional findings indicate that the 10-year Treasury rate is not purely a random walk. Within the autoregressive integrated moving-average (ARIMA) modeling framework, a purely random walk series is characterized as ARIMA (0, 1, 0). The rate on 10-year Treasury, however, can best be described as an ARIMA (0, 1, 1) process. We shall argue that the existence of the first-order moving-average term is not inconsistent with bond market efficiency. Moreover, we can think of the mortgage rate as being made up of the rate on 10-year Treasury plus a prepayment premium. As we shall see, the prepayment premium can also best be described as ARIMA (0, 1, 1). This, consistent with our findings, implies that the 30-year mortgage rate should replicate the stochastic behavior of the 10-year Treasury rate and follow an ARIMA (0, 1, 1) process. This paper is organized as follows: Section 2 describes the random walk model. Section 3 presents our forecast evaluation results. Section 4 first explores the relation between the rates on 30-year mortgage and 10-year Treasury and then examines whether the random walk forecasts of the prepayment premium are of value to a user. Section 5 summarizes our findings.

In line with the implications of term structure theory in an efficient bond market, we formulate a random walk model that generally produces unbiased and efficient forecasts of the US 30-year home mortgage rate for 1987–2006. Forecast accuracy improves with a reduction in lead time but deteriorates with an increase in the forecast horizon. We find, however, no clear trend indicating that forecast accuracy has improved over time. From a more practical perspective, the random walk forecasts of the 30-year mortgage rate and prepayment premium accurately predict directional change and thus are of value to a user. Given our findings, we may argue that market participants and policymakers should consider using the proposed random walk forecasts of the 30-year mortgage rate in decision-making. Although term structure theory suggests that the random walk forecasts of long-term interest rates are optimal, we still suggest future research to look for leading indicators that could help improve forecast accuracy over the random walk forecasts studied here.