Hypothesis Testing in ARIMA(p, 1, q) Models

Saïd, Saïd E.; Dickey, David A.

doi:10.1080/01621459.1985.10478125

Cited by 94 publications

(17 citation statements)

References 11 publications

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“…An ADF test (Dickey and Fuller, , ) and a Phillips–Perron test (1988) were used. The ADF test is used in the following equation:

y_{normalt} = α + ρ {normaly}_{t - 1} + β t + {normalΣ}_{i = 1}^{k} c_{normali} Δ y_{t - i} + ε_{normalt},

where y t is the series of relative spreads, t is a linear trend, and k is the number of lags included in the estimated equation in order to deal with a possible auto‐correlation and to increase the test reliability (Dickey and Fuller ; Saïd and Dickey, ). The number of lags, k , is chosen in order to minimize the Schwarz information criterion .…”

Section: Statistical Tools: Determining and Dating Investor Reactionmentioning

confidence: 99%

European Rating Actions, Investor Reaction, and Bond Spread Volatility

Ory¹,

Raimbourg²

2015

Economic Notes

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This paper uses unit root tests that allow for structural breaks in order to examine the impact of ratings announcements on European bond credit spreads. In general, there are no noticeable reactions to announcements for issues in euros, which comes in contrast to the results of previous studies on US corporate bonds. However, we have noticed a reaction to rating actions for issues in sterling. In the case of a reaction to a downgrade or a negative watch, investor reaction generally occurs before the rating announcement, and negative watches are anticipated by investors a little more frequently than downgrades. For this type of event, we see a decrease in spread volatility after the rating announcements, as if the action of the rating agency confirms the informed investors' perception of default risk, and in doing so, stabilizes spreads and reduces spread volatilities.(J.E.L.: G14, G33).

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“…An ADF test (Dickey and Fuller, , ) and a Phillips–Perron test (1988) were used. The ADF test is used in the following equation:

y_{normalt} = α + ρ {normaly}_{t - 1} + β t + {normalΣ}_{i = 1}^{k} c_{normali} Δ y_{t - i} + ε_{normalt},

Section: Statistical Tools: Determining and Dating Investor Reactionmentioning

confidence: 99%

European Rating Actions, Investor Reaction, and Bond Spread Volatility

Ory¹,

Raimbourg²

2015

Economic Notes

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“…When the true model is a random walk, Fuller (1976) and Dickey & Fuller (1979, 1981 derived the distributions of unit root tests when the estimated model is (i) the true model, (ii) a random walk with shift in mean, (iii) a random walk with shift in mean and a linear time trend. Said & Dickey (1985) derive the limiting distribution of the appropriate test statistic when the time series is an autoregressive integrated moving average process of order (p, 1, q), hereafter denoted by ARIMA (p, 1, q), with known p and q. Such a restriction is a considerable drawback in applying these tests to economic time series for which there is considerable evidence of the presence of moving average terms (Schwert, 1987).…”

Section: Introductionmentioning

confidence: 99%

Testing for a Unit Root in the Presence of Moving Average Errors

Hall¹

1989

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY In this paper we propose a new approach to testing for unit roots in a time series {Yt} with moving average innovations based on an instrumental variable estimator. If {Yt} is a random walk with moving average innovations, we derive the limiting distribution of the instrumental variable estimator when the estimated model is either (i) the true model, (ii) a random walk with shift in mean, or (iii) a random walk with shift in mean and a linear time trend. These distributions are identical to those tabulated by Dickey & Fuller (1979, 1981) in some cases, and easily transformed, in the spirit of Phillips (1987), to the Dickey & Fuller distributions in others. Some key words: Instrumental variable estimator; Moving average error; Time series; Unit root. This content downloaded from 195.78.

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“…We first examine whether the variables of interest are difference stationary. Several unit root tests are employed: the augmented Dickey–Fuller (ADF) test (τ‐statistic) (Said and Dickey, 1984,1985), the Phillips–Perron (PP) test ( Z ( t α )) (Phillips and Perron, 1988), and the J( p , q ) test of Park and Choi (1988) and Park (1990), which is based on the variable addition approach, employing polynomial time trends as superfluous regressors. These tests are based on the null of a unit root against the stationarity alternative.…”

Section: Test Resultsmentioning

confidence: 99%

Quasi‐fixed inputs and long‐run equilibrium in production: a cointegration analysis

Kim

Lee

2001

J of Applied Econometrics

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This paper proposes a cointegration approach to testing the validity long-run equilibrium in production, where capital and labour are taken as quasi-fixed inputs. Previous studies consider only capital as the quasi-fixed input and do not take account of the time series properties of the variables, assuming implicitly that they are stationary. The canonical cointegrating regressions (CCR) procedure is employed to test for cointegration in both the single-equation and the seemingly unrelated regressions framework, and long-run equilibrium conditions are tested. The evidence from US manufacturing reveals that capital and labour are not fully adjusted to their long-run optimal values, casting doubt on the long-run equilibrium hypothesis. Copyright K 6 4 A theoretical discussion of a short-run model based on the variable cost function is provided by Brown and Christensen (1981); see also Caves, Christensen, and Swanson (1981). 5 This specification of the stochastic cost function is an adaptation of McElroy (1987) and Brown and Walker (1995). Their analysis, however, rests on the long-run cost function and does not allow for stochastic properties of the time series. 8 Thus long-run equilibrium is viewed here as an average relationship. Kulatilaka (1985), however, views it as holding for every observation. 9 This study probably represents the first real application of the system-based CCR procedure within the context of SUR. Ogaki and Park (1998) and Ogaki (1992) also apply the system-based CCR procedure, but in a slightly different form mainly to deal with a cointegrated system with a trend stationary process. For applications of the single-equation CCR procedure, see Fisher and Park (13 Park (1990, p. 119) shows that the asymptotic distribution of the Wald tests using random walk processes is 2 distributed asymptotically. Referees, however, point out that this result could be interpreted as ad-hoc evidence, since the asymptotic behaviour of the simulation-based tests is not yet examined. 14 The H(0,1) test indicates that the null hypothesis is not rejected for all cases, except for a pair of ln P k and ln P Ł K for which the null is marginally rejected at the 5% level, but not at the 2.5% level.

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Hypothesis Testing in ARIMA(p, 1, q) Models

Cited by 94 publications

References 11 publications

European Rating Actions, Investor Reaction, and Bond Spread Volatility

European Rating Actions, Investor Reaction, and Bond Spread Volatility

Testing for a Unit Root in the Presence of Moving Average Errors

Quasi‐fixed inputs and long‐run equilibrium in production: a cointegration analysis

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