Spurious Regression and Trending Variables*

Noriega, Antonio E.; Ventosa‐Santaulària, Daniel

doi:10.1111/j.1468-0084.2007.00481.x

Cited by 33 publications

(17 citation statements)

References 15 publications

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“…The LS regression has therefore been estimated using only observations from the first quarter of 1981 through the third quarter of 2001:

\begin{matrix} falsenone none none nonefalsearray \\ arrayleft \log {MathClass-open({GDP}_{UK} MathClass-close)}_{t} = & arrayleft α + & arrayleft β x_{t} + & arrayleft γ_{1} {DU}_{t} + & arrayleft γ_{2} {DT}_{t} + ϵ_{t} \\ arrayleft & arrayleft 11.95 & arrayleft - 0.003 & arrayleft - 0.07 & arrayleft - 0.002 \\ arrayleft & arrayleft MathClass-open(2848 MathClass-close) & arrayleft MathClass-open(- 39.04 MathClass-close) & arrayleft MathClass-open(- 11.36 MathClass-close) & arrayleft MathClass-open(- 6.54 MathClass-close) \end{matrix}

where DU t accounts for the change in level and DT t for the change in trend. Note that the R 2 is quite high (0.9918) and the classical

scriptF

statistic (26.4489) rejects the null hypothesis of β = γ 1 = γ 2 = 0, which is in line with what is known about spurious regression between BTS processes (see Noriega and Ventosa‐Santaulària, ). We next forecast the UK GDP series using the estimates of the spurious regression .…”

Section: Forecasting the Gdp Of The United Kingdomsupporting

confidence: 80%

“…Spurious regression has been well documented in econometrics since Phillips () provided the asymptotic arguments that explain it. It occurs whether the variables are—independently—generated as driftless unit roots (Phillips, ), unit roots with drift (Entorf, ), integrated of higher‐order processes (Marmol, , ), long‐memory processes (Cappuccio and Lubian, ; Marmol, ) or (broken)‐trend stationary processes (Hassler, ; Noriega and Ventosa‐Santaulària, , ).…”

Section: Introductionmentioning

confidence: 99%

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Spurious Forecasts?

Martínez-Rivera

Ventosa‐Santaulària

Vera-Valdés

2011

Journal of Forecasting

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Phillips (1998) demonstrated that deterministic trends are a valid representation of an otherwise stochastic trending mechanism; he remained skeptic, however, about the predictive power of such representations. In this paper we prove that forecasts built upon spurious regression may perform (asymptotically) as well as those issued from a correctly specified regression. We derive the order in probability of several in-sample and out-of-sample predictability criteria (F test, root mean square error, Theil's U-statistics and R 2 ) using forecasts based upon a least squares-estimated regression between independent variables generated by a variety of empirically relevant data-generating processes. It is demonstrated that, when the variables are mean stationary or trend stationary, the order in probability of these criteria is the same whether the regression is spurious or not. Simulation experiments confirm our asymptotic results.

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“…The LS regression has therefore been estimated using only observations from the first quarter of 1981 through the third quarter of 2001:

\begin{matrix} falsenone none none nonefalsearray \\ arrayleft \log {MathClass-open({GDP}_{UK} MathClass-close)}_{t} = & arrayleft α + & arrayleft β x_{t} + & arrayleft γ_{1} {DU}_{t} + & arrayleft γ_{2} {DT}_{t} + ϵ_{t} \\ arrayleft & arrayleft 11.95 & arrayleft - 0.003 & arrayleft - 0.07 & arrayleft - 0.002 \\ arrayleft & arrayleft MathClass-open(2848 MathClass-close) & arrayleft MathClass-open(- 39.04 MathClass-close) & arrayleft MathClass-open(- 11.36 MathClass-close) & arrayleft MathClass-open(- 6.54 MathClass-close) \end{matrix}

where DU t accounts for the change in level and DT t for the change in trend. Note that the R 2 is quite high (0.9918) and the classical

scriptF

Section: Forecasting the Gdp Of The United Kingdomsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Spurious Forecasts?

Martínez-Rivera

Ventosa‐Santaulària

Vera-Valdés

2011

Journal of Forecasting

Self Cite

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“…From the literature focusing on the traditional I(0)/I(1) unbalanced regression setup with exogenous regressors and i.i.d. innovations we know that the t-statistic is well behaved and converges to a standard normal random variable, as shown in Noriega and Ventosa-Santaulària (2007) and successively in Stewart (2011). Theorem 1 proves that the same result holds true in our I(0)/I(d) specification.…”

Section: Ordinary Least Squares Estimationsupporting

confidence: 61%

Unbalanced Regressions and the Predictive Equation

2015

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Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness in the theoretical predictive equation by suggesting a data generating process, where returns are generated as linear functions of a lagged latent I(0) risk process. The observed predictor is a function of this latent I(0) process, but it is corrupted by a fractionally integrated noise. Such a process may arise due to aggregation or unexpected level shifts. In this setup, the practitioner estimates a misspecified, unbalanced, and endogenous predictive regression. We show that the OLS estimate of this regression is inconsistent, but standard inference is possible. To obtain a consistent slope estimate, we then suggest an instrumental variable approach and discuss issues of validity and relevance.Applying the procedure to the prediction of daily returns on the S&P 500, our empirical analysis confirms return predictability and a positive risk-return trade-off.

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“…505-506. and in Noriega and Ventosa-Santaularia (2007). The last sum, DT yt DT zt , is not needed in this example, but it appears in other combinations; we assume, for simplicity, that λ y > λ x > λ z .…”

Section: A Proof Of Propositions 1 and 2 And Corollarymentioning

confidence: 99%

“…Indeed, the order in probability of tδ Noriega and Ventosa-Santaulària (2006) and Noriega and Ventosa-Santaularia (2007)]. In this paper, we are concerned with the estimation of equation (1) by Instrumental Variables (hereinafter, IV).…”

Section: Estimates Using Nonstationary Variablesmentioning

confidence: 99%

Spurious Instrumental Variables

Ventosa‐Santaulària

2010

Communications in Statistics - Theory and Methods

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Spurious regression phenomenon has been recognized for a wide range of Data Generating Processes: driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity, etc. The usual framework is Ordinary Least Squares. We show that the spurious phenomenon also occurs in Instrumental Variables estimation when using non-stationary variables, whether the non-stationarity component is stochastic or deterministic. Finite sample evidence supports the asymptotic results.

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Spurious Regression and Trending Variables*

Cited by 33 publications

References 15 publications

Spurious Forecasts?

Spurious Forecasts?

Unbalanced Regressions and the Predictive Equation

Spurious Instrumental Variables

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