This note presents cointegration tests of variables relevant in formulating a forecasting equation for the share of ARMs (adjustable rate mortgages) in home mortgage originations. Previous work by Ryding [FRBNY Quarter ly Rev iew, 1990] relied on a small sample-quarterly data over a sixyear period. Here over 100 seasonally unadjusted monthly observations (1982:1-1992:2) are used to closely relate the application to large-sample cointegration theory. Let II, be the ARM share of mortgages originated at time t, X, the 3-month T-bill rate, and Z, the rate on the 10-year Treasury bond. Under the null H0: p = I, given the general nth-order autoregressive process ~b(B)(1 p B ) Y t ~b(1)(1 p)bt = e t where the error term e t is N/D(0, a2), B is the backshift operator, ~b(B) = (1 p l B • • • "pnBn), and # = E(Y,), the regression of VY~ on 1, Y,. ~, VY,. l . . . . . VY,.n +~ (where V = I B) produces a consistent estimate of the coefficient of Y,. ~ and a t-statistic whose limit distribution is the one-degree-of-freedom test 1"~ of Fuller [Introduction to Stat is t ical Time Series, 1976] and Dickey and Fuller [JASA, 1979]. A large value for this augmented Dickey-Fuller (ADF) test statistic rejects the null suggesting Y~ is integrated of order zero, i.e., 1(0). For n = 2, the above model reparameterizes to VY, = (Pi + P2 1)(]I, #) -p2VYt. 1 + e, so that under the null the unit root test involves regressing VY~ on 1, Y,. t, and VY,. i and obtaining the t-test for the coefficient of Y,. i. For Y,, the ADF statistic for the regression coefficient of Y,t, assuming an AR(2) process, was -1.99. This is less than the approximate 5 percent critical value of -2.81 in Fuller [1976], indicating that Y~ is 1(1). For X, the ADF under AR(2) was -3.32, suggesting that the 3-month T-bill rate is I(0). The corresponding result for Z, was -2.37, implying the series is I(1). Similar tests for the yield curve variable Z, X , found it to be I(1). This last result seems consistent with the proposition that the sum (or difference) of an I(1) and I(0) series will be I(1). The following cointegrating regressions were fitted: Y, = c~o + t~t(Z, X , ) + ~h, and VY, = [3o + [3t(Z, X , ) + 72,. The cointegrating regression Durbin-Watson statistics for the null that DW = 0, with respect to the residuals ~t, and ~2,, were 0.11 and 1.37, respectively. Given that the approximate 1 percent critical value for this test statistic is 0.51, the null of non-cointegration between VY~ and (Z, X , ) is rejected while that between Y~ and (Z, X,) is accepted. The ADF for the residuals ff~, and ~2, under AR(2) were -2.02 and -6.06, respectively. The latter exceeds the 1 percent critical value of -3.77 indicating that the residual ~z, is 1(0) and suggesting once more that VY, and (Z, X , ) are cointegrated. Additional lags in the unit root tests of the residuals did not alter these results. Thus, Y, has to enter in first-differenced form in a forecasting equation with ( Z , X , ) as an explanatory variable.