However, there are more and more evidences showing that many economic and financial time series have the characteristics of long memory series. And some studies reveal that **spurious** regression do not only for independent random walks but also for long memory processes, such as Marmol (1998) and Tsay and Chung (2000). It demonstrated that **spurious** correlations are evident in regression involving combinations of long memory I (d) series, with d being a fractional number. However, it has been acknowledged that structural changes in the mean of time series can easily be confused with long memory dependence. Hence, the purpose of this paper is to investigate the possible existence of **spurious** **relationship** with a pair of stationary long memory processes with mis-specified change points, which could take place at different points in time.

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This paper analyzes **spurious** regression phenomenon involving AR(p) stable processes with trend breaks. It shows that when those time series are used in ordinary least squares regression, the convenient t-ratios procedures wrongly indicate that the **spurious** **relationship** is present as the pair of independent stable series contains trend changes. The **spurious** **relationship** becomes stronger as the sample size approaches to infinite. As a result, **spurious** effects might occur more often than we previously believed as they can arise even between AR(p) stable series in present of trend breaks.

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This paper seeks to make three contributions to theory on the job satisfaction-job performance **relationship**. First and foremost, it will provide a large-scale empirical test of a causal model in which the satisfaction-performance **relationship** is specified as **spurious**. This test is based upon meta-analytic data compiled from multiple study effects, and representing many employed individuals. This is a valuable contribution because it will help to specify the mechanism underlying a **relationship** that has received much empirical support, but lacks clarity as to why the variables are related. Also, a **spurious** **relationship** between job satisfaction and job performance would suggest that the causal effects between satisfaction and performance, both unidirectional and

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three particular examples, the diﬀerence between the simulated and the theoret- ical statistics is greater when the break dates are closer to the sample endpoints (right panel). Although in can not be inferred from the ﬁgure, our numerical simulations show that, for a sample size as small as 25 observations, the values of the t-statistic (both theoretical and simulated) are greater than 5.0, for all three analyzed examples, indicating a **spurious** **relationship** between y t and x t .

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Part a) of the theorem shows that, as expected, when both variables are I(0), the **spurious** regression phenomenon is not present, since the t-statistic collapses to zero (at rate √ T ). Part b) indicates that when one of the variables is I(0) while the other follows any of the other nonstationary cases, the t-statistic neither collapses to zero, nor it diverges to infinite; instead, it converges (to a constant, or to a random variable, depending on the DGP s. See the small sample results of next section). For the majority of combination of cases, the t−statistic diverges (at rate √ T or faster), indicating a **spurious** **relationship** among independent variables, as parts c)-e) show.

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Parts f ) of the theorems show that the **spurious** regression parameter t- statistic only diverges to in ﬁ nity under structural breaks; otherwise, it has a well de ﬁ ned limit. Hence, a **spurious** **relationship** will be present only under DGP i3, i = A, B. Note that, as opposed to the case of no trend in the re- gression, the **spurious** regression coeﬃcient (and its t-statistic) converges to the same distribution across DGP s ij, i = A, B; j = 1, 2. Table A1 in the Appen- dix presents a summary of results concerning orders in probability of relevant statistics.

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167 GPS sites, derived from the weekly SINEX file solutions of the IGS. They noticed spectral peaks and a comb of harmonics that coincided with a so-called ‘‘GPS draconitic year’’ (abbreviated here as dy), being the 351.4 days required for a GPS orbit to repeat its inertial orientation with respect to the sun. The energy found at this period and its harmonics was not found in solutions from other space geodetic techniques nor geophysical data [Ray et al., 2008]. Given that this period is close to the solar year (365.25 days), it is likely that the probable **spurious** draconitic signals will bias estimates of real geophysical phenomena that operate at seasonal (solar) timescales (for example, seasonal hydro- logical cycles). Ray et al. [2008] suggested that the causes for the draconitic signals lie in **spurious** aliasing and/or orbital errors or aliasing/propagation of site-dependent effects such as multipath.

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Fig. demonstrates the engineering chart for the proposed VMFU in which the SPST altered Booth encoder has been appeared in Fig. 10. The VMFU can be generally disintegrated into three areas, i.e., the Partial Product Generation, the Partial Product Reduction (PPR), and the Accumulation (ACC) segments. At the point when the operand other than the Booth encoded one has a little supreme esteem, there are chances to decrease the **spurious** power dispersed in the pressure tree in the PPR segment. As indicated by the examination of the expansion appeared in Figs. 3 and 9, we supplant a portion of the adders in the pressure tree of the VMFU, which include the PP0 to PP3, with the SPST-prepared adders. In addition, the viper in the ACC segment is likewise supplanted with the SPST-prepared snake. This snake is utilized to aggregate the increase brings about the MAC operation and register the interjection, SAD, expansion, and subtraction. These adders are set apart with diagonal lines as appeared in Fig. 11 with their bit widths of the MSP and LSP demonstrated, separately, in the numerator and the denominator of the nearing division esteems.

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emphasized that **spurious** estimated relationships occur not only between (or among) random- walk or “integrated” variables, but also stationary but highly autocorrelated time series variates. Consequently, Davidson and MacKinnon (2004, p. 611) have included results analogous to those of theirs reported above but with the two basic series generated not by random walks, but by first-order autoregressive (AR) processes, using an AR parameter value of 0.8. In this case the Davidson and MacKinnon rejection values are reported only in graphical, not numerical, form so the reporting of them in row one of Table 2, below, can be only approximate. The values from my own 10,000 simulations given in row two are, however, in full accord. These rejection frequencies do not rise with sample size, as in the random-walk cases of Table 1, but are greater than 1/3 in all of our simulations—over six times as large as the true rejection probability. But, as before, almost all of the test regressions have DW statistic values smaller than 1.0.

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The present paper extends the analysis of Phillips (1986) to nonparametric regression …tting. The results show that all the usual characteristics of linear **spurious** regression are manifest in the context of local level regression, including divergent signi…cance tests, local goodness of …t, and Durbin Watson ratios converging to zero. There is therefore a need for local diagnostic procedures to assist in validating nonparametric regressions of this type. Some global tests for nonlinear cointegration have recently been developed for parametric models. For example, Hong and Phillips (2006) developed a RESET test for nonlinearity in cointegrating relations and Kasparis (2006) developed a CUSUM test for functional form misspeci…cation in cointegration.

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The goal of this paper was to introduce some general issues of non-stationarity for practitioners, students and beginning researchers. Using elementary techniques we examined the effect of non-stationary data on the results of regression analysis. We further shoved the effect of larger sample sizes on the spuriousness of regressions and we also examined the well known “rule of thumb” of how to identify **spurious** regressions. We also demonstrated the problem of **spurious** regression on a practical example, using closing prices of stock market indices from CEE markets.

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the impact of conditioning associated with the deﬁnition of switching points on the statistical properties of ﬁnancial returns. Our ﬁnding applies directly to the volatility. For volumes[r]

had preconceived notions of case and control definitions, not one of the surveys had a written protocol to define precisely, before the initiation of data acquisition, the criteria under[r]

Bengio et al. (2009) and Kumar et al. (2010) de- veloped training paradigms which are inspired by the learning principle that humans can learn more effectively when training starts with easier con- cepts and gradually proceeds with more difficult ones. Since easiness of information is not read- ily available in most datasets, previous approaches used heuristic techniques (Spitkovsky et al., 2010; Basu and Christensen, 2013) or optimization algo- rithms (Jiang et al., 2015, 2014) to quantify easi- ness for instances. These approaches consider an instance as easy if its prediction loss is smaller than a threshold ( λ ). Given a neural network as the learner, we adopt curriculum learning to iden- tify **spurious** instances as follows (see Figure 2):

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Economic models often imply that certain variables are cointegrated. However, tests often fail to reject the null hypothesis of no cointegration for these variables. One possible explanation of these test results is that the error is unit root nonstationary due to a nonstationary measurement error in one variable. A nonstationary error in one variable leads to a **spurious** regression when the true value of the variable and the other variables are cointegrated. In the unit root literature, when the stochastic error of a regression is unit root nonstationary, the regression is called a **spurious** regression. This is because the standard t test tends to be spuriously significant even when the regressor is statistically independent of the regressand in Ordinary Least Squares. Monte Carlo simulations have often been used to show that the **spurious** regression phenomenon occurs with regressions involving unit root nonstationary variables (see, e.g., Granger and Newbold (1974), Nelson and Kang (1981, 1983)). Asymptotic properties of estimators and test statistics for regression coeﬃcients of these **spurious** regressions have been studied by Phillips (1986, 1998) and Durlauf and Phillips (1988) among others. For example, currency held by the domestic economic agents for legitimate transactions is very hard to measure due to currency held by foreign residents and black market transactions. Therefore, money may be measured with a nonstationary error. As shown by Stock and Watson (1993) among others, if the money demand function is stable in the long-run, we have a cointegrating regression when all variables are measured without error. If the variables are measured with stationary measurement errors, we still have a cointegrating regression. However, if money is measured with a nonstationary measurement error, we have a **spurious** regression. We can still recover structural parameters under certain conditions for the nonstationary measurement error.

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Abstract—A wideband interdigital capacitor (WIDC) is proposed and veriﬁed. By short interconnecting the open ends of interval ﬁngers with microstrip lines etched on PCB bottom layer, the **spurious** spikes that limit the bandwidth of conventional interdigital capacitor (IDC) are eliminated. The bandwidth and capacitance of IDC increase more than 2800% and 100%, respectively.

DOI: 10.4236/ojs.2017.75054 776 Open Journal of Statistics short-memory AR(1) variance correction and the RIA analysis utilizing a permutation test returns a significant intervention effect when in fact no intervention occurred. A possible explanation for this is the presence of strong correlation in the data, perhaps long-memory, which could have produced the **spurious** detection of a significant intervention effect. The observations in the following examples are only approximately equally spaced in time. They were assumed so in order to simplify the analyses.

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starting time t iff. the increments were stationary, iff. z=x(t,T)=x(T) independent of the starting time t. But the increments in finance data are not stationary [2], and there is no ergodicity in a nonstationary (i.e., far from statistical equilibrium) time series, so that the sliding window method produces ‘significant artifacts’, **spurious** stylized facts. We emphaize that FX markets are a nonstationary stochastic process with nonstationary increments. All assumptions of stationarity fail miserably whe it comes to market data.

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Of course, casual observation also reveals many cases in which producers and retailers contravene established conventions as a profit-seeking strategy. For example, supermarkets sometimes place their ‘special offers’ away from the shelves used to display similar but normally-priced goods. It would be naïve to deny that in many such cases, retailers are seeking to exploit consumers’ cognitive limitations. However, competition surely restricts the scope for this kind of obfuscation. If consumers find it easier to get value for money when they shop in supermarkets which use standardised layouts, they will tend to patronise supermarkets that are laid out in standard ways; retailers who try to entrap customers by using unfamiliar layouts will lose business. Intuitively, it seems that we are observing a balance of forces, some of which favour the emergence of common standards while others favour deviation from those standards. The existing literature on **spurious** complexity has concentrated on the latter. Our paper is an attempt to redress the balance.

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In both cases the language of flood and of the rivers derives from a common ancient Near Eastern and biblical vocabulary of military defeat, coloured by the conception of royal battle as[r]

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