the joint limiting distribution of the residual autocorrelation functions and the ab- solute residual autocorrelation functions, where the residual is obtained from model (1.1)-(1.2) fitted by the QMELE approach. Based on this, we propose a mixed port- manteau **test** statistic for model (1.1)-(1.2). Via some simplifications, we can show that our mixed **portmanteau** **test** nests two **portmanteau** tests Q r and Q a in Li

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The paper studies the estimation and the **portmanteau** **test** for double AR(p) model with Laplace(a, b) distribution. The double AR(p) model is investigated to propose ﬁrstly the quasi-maximum exponential likelihood estimator, design a **portmanteau** **test** of double AR(p) on the basis of autocorrelation function, and then establish some asymptotic results. Finally, an empirical study shows that the estimation and the **portmanteau** **test** obtained in this paper are very feasible and more eﬀective.

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F or eah of these N = 1, 000 repliations we tted a V ARMA (1, 1) model and perform standard and modied LB **test** based on m = 1, . . . , 4 , 6 and 10 residual autoorrelations. The adequay of the V ARMA (1, 1) model is rejeted when the p -value is less than 5% . F or this partiular weak V ARMA model, we have seen that the atual level of the standard version is generally

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After identification and estimation of the parameters in a fitted model, the good- ness of fit **test** is the next most important step for testing the selected model. In time series analysis, we assume that the series is stationary with white noise innovations. This implies that a good fitted model must produce residuals that are approximately uncorrelated in time. Box and Pierce (1970) show that the asymptotic distribution of the residual autocorrelations can be utilized to check the validity of this assumption under the ARMA models. They introduced to the literature the overall goodness- of-fit **test** on the residuals autocorrelations up to lag m. This **test** statistic is called **portmanteau** **test**. Since then there evolves many literature on **portmanteau** tests for ARMA and GARCH models (Ljung and Box, 1978; McLeod and Li, 1983; Peˇ na and Rodriguez, 2002; Rodr´ıguez and Ruiz, 2005; Peˇ na and Rodriguez, 2006). The **portmanteau** **test** is extended to the multivariate VARMA models by Chitturi (1974, 1976); Hosking (1980); Li and McLeod (1981); Francq and Ra¨ısi (2007) and to the MGARCH models by (Li and Mak, 1994; Ling and Li, 1997). Lin and McLeod (2006) introduce the Monte-Carlo **portmanteau** **test** and show that this **test** provides a **test** with the correct size. They show that the Monte-Carlo version of Peˇ na and Rodriguez (2002) is often more powerful than its competitors. Lin and McLeod (2008) extends the Monte-Carlo **test** of Peˇ na and Rodriguez (2002) to the ARMA models with stable Paretian errors.

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Recently, a large number of research papers attempted to weaken the assumption of strong white noise for the **portmanteau** **test** (Romano and Thombs, 1996; Francq and Zakoïan, 1998; Francq et al., 2005). In order to solve this problem of non-i.i.d. noise, some researchers (Chen and Deo, 2004; Deo, 2000) derived the spectral density **test** for the martingale di ﬀ erence hy- pothesis in the presence of conditional heteroscedasticity. Later, Lobato et al. (2001, 2002) addressed the problems to **test** the null hypothesis with time series to uncorrelated up to a fixed order m and proposed a modified Box-Pierce **test** for this null hypothesis. However, these tests do not solve the problem of weak white noise including the important special case of GARCH innovations. Francq et al. (2005) successfully derived the distribution of the residuals under the null hypothesis of uncorrelated, but not independent errors and then proposed another mod- ification for Box-Pierce **Test** similar to McLeod (1978). They show the advantages and better performance of their tests compared to the original **portmanteau** tests.

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Many opportunities of future research are available. The plan of the future research on **portmanteau** tests for the residuals autocorrelation diagnostics in ARMA models can be split into four main areas. First, extension of the **portmanteau** tests for seasonal, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Threshold Autoregressive (TAR) models. Second, extend the research to examine the relationship between ARMA(p,q) coefficients and the power of the tests for testing the goodness-of- fit tests in time series. Third, one may study a **portmanteau** **test** that combines Monti Q ɶ M and Ljung–Box

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Since Box and Pierce (1970) paper, the **portmanteau** **test** has become the vital part of time series diagnostic checking. Several modifications and versions of Box and Pierce (1970) has been suggested in the literature, see e.g. Ljung and Box (1978), McLeod and Li (1983), Monti (1994), Katayama (2008), Katayama (2009). These tests are capable of testing the significance of autocorrelation (partial autocorrelation) up to a finite number of lags. Chand et al. (2012) has used the **portmanteau** tests to criticize the fitted models. In the discussion of Prothero and Wallis (1976), Chatfield has mentioned the poor power properties of Q m and has recommended focusing on residual autocorrelations at the first

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Both multivariate **portmanteau** tests (with the lag value p = 12) of Li & Mcleod (1981) and Reinsel (1997, p.149) for the residuals from the above fitted vector AR(1) model are insignificant at the 5% level. The univariate **portmanteau** **test** is insignificant at the level 5% for three (out of the four) component residual series, and is insignificant at the level 1% for the other component residual series. On the other hand, a vector AR(2) model was selected by the AIC for the 4 factor series with vector AR(1) as its closest competitor. In fact the AIC values are, respectively, 240.03, 0.11, 0.00, 6.38 and 18.76 for the AR-order 0, 1, 2, 3 and 4.

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Finally, we suggest three future subjects, which may lead to some better specifi- cation tests. First, as in Escanciano and Lobato (2009), it is of interest to consider the case that m is not fixed but optimally chosen by the data set. If it is possible, a more powerful testing procedure should be expected. Second, till now, less is known to choose the optimal weight matrix W (in some sense) such that the corresponding weighted Ljung-Box or Monti **portmanteau** **test** has the best performance among all weighted **portmanteau** tests in strong ARMA models. We may expect that the merits of this optimal weighted **portmanteau** **test** still hold in weak ARMA models. Third, since all **portmanteau** tests still need a selection of m, they can not detect serial corre- lations beyond lag m. Hence, it is a practical demand to study the Cram´er-von Mises spectral **test** (e.g., Shao (2011b)) which can detect serial correlations at all lags.

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The hardware used in this paper for generating the primary input sequence A consists of a linear-feedback shift-register (LFSR) as a random source [17], and of a small number of gates (almost six gates are needed for every one of the benchmark circuits considered). The gates are used for modifying the random sequence in order to avoid cases where the sequence takes the circuit into the same or similar reachable states repeatedly. This is referred to as repeated synchronization [18]. In addition, the on-chip **test** generation hardware consists of a single gate that is used for determining which tests based on will be applied to the circuit. The result is a simple and fixed hardware structure, which is tailored to a given circuit only through the following parameters.

We compared 2 relatively brief, portable, low cost **test** of CV endurance & functional status with the potential for broad field application. Although the SMWT is well established and highly recommended in clinical setting, but many clinical setting but many clinical settings may look on unobstructed corridor of adequate length even the course is shortened to 30feet (ATS, 2002). We made efforts to examine the result of SMWT & STST, which requires less space when compared to SMWT. Therefore, the purpose of the study was to compare the utility of the STST to that of SMWT in the evaluation of the CV endurance in patient with COPD. In the literature STST is generally used to determine the functional status of elderly patient with orthopedic diseases (Millington et al., 1992; Gross et al., 1998; Lord Sr et al., 2002; Lindemann et al., 2003; Jones et al., 1999; Scarborough et al., 1999). The SMWT is usually used for patients with COPD. The timed walk distance has been demonstrated to be a strong predictor (Bowen et al., 2000; Stel et al., 2001; Torres et al., 2002; Pinto- Plata et al., 2004; Guyatt et al., 1985; Scarborough et al., 1999) & survival in patient with COPD, therefore, we consider that STST would determine the CV endurance as the SMWT in patient with COPD.

It must be noted here that a small degree of anxiety is normal and even necessary to do things. This fact should be considered that anxiety is very beneficial at normal levels (Csizér & Piniel, 2013), the point is that less anxious students will be more successful than the more anxious students because the former group is more spontaneous, more creative and have better judgment, but the latter ones are very careful about their errors, consume more time solving a problem and check the problems several time and finally cannot recognize their thoughts creatively (Çubukçu, 2008). Anxious learners do not volunteer to answer questions or to participate in classroom activities. These students always complain that their class moves too quickly and they are left behind. It is natural because the anxious students require more time for learning. These factors aeffect not only on learning but also on **test** taking, they cannot perform well, they do not have enough time and they cannot remember the things, which they have learned before (Tsai, 2013). Anxious students use simple structures in their speaking, this problem will cause these students not to be able to communicate in the second language (Oxford, 1999).

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than LH, sometimes to frankly elevated concentration. Although the mechanisms responsible are not entirely clear, evidence suggests that the smaller follicular cohorts in aging women produce less inhibin-B and estradiol, resulting in less negative feedback inhibition on Clomiphene induced pituitary FSH release. The Clomiphene challenge **test** can identify women who might otherwise go unrecognized if evaluated by basal cycle day 3 FSH and estradiol levels alone. The likelihood of successful pregnancy is inversely related to both the cycle day 3 and day 10 FSH levels. More importantly, however, in women with a normal day 3 FSH level, a high day 10 value has the same poor prognosis as an elevated day 3 FSH concentration. The stimulated day 10 estradiol level has no prognostic value. An elevated cycle day 3 FSH level or abnormal Clomiphene challenge **test** correlates consistently with a poor prognosis for I.V.F. success (less than 10%), regardless of age (Leon speroff et al., 2005; EI- Tonkhy et al., 2002). These and other observations indicate that age and ovarian reserve **test** results are independent predictor of I.V.F. outcome and, by inference, general fecundability. The prognosis for women with an abnormal OR **test** is generally poor, even if they are young. In contrast, the prognosis for women with normal **test** results relates to their age; a normal **test** result does not improve the poorer, age-specific prognosis for older women (Leon speroff et al., 2005; Scott et al., 1998). Women with low cycle day 3 FSH levels generally exhibit less between cycle variability than women with higher levels. Numerous other methods for measuring OR have been investigated including; ovarian volume and early follicular phase antral follicle counts; basal and clomiphene or exogenous FSH – stimulated inhibin B-levels; response (FSH, estradiol, inhibin-B) to stimulation with a GnRH agonist or human menopausal gonadotropin; and basal and GnRH agonist or gonadotropin stimulated anti mullerian hormone levels (Leon speroff et al., 2005; Tietze, 1957). The number of small antral follicles observed by TVUS examination at the onset of the menstrual cycle reflects the size of the resting follicular pool, and correlates with age and response to gonadotropin stimulation ; observation of 10 or fewer follicles is associated with increased risk of cycle cancellation low basal or stimulated inhibin –B levels suggest a low OR, but studies of their productive value have yielded conflicting result (Leon speroff et al., 2005; Smotrich et al., 1995).

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Portmanteaus are a word formation phe- nomenon where two words are com- bined to form a new word. We pro- pose character-level neural sequence-to- sequence (S2S) methods for the task of **portmanteau** generation that are end-to- end-trainable, language independent, and do not explicitly use additional phonetic information. We propose a noisy-channel- style model, which allows for the incorpo- ration of unsupervised word lists, improv- ing performance over a standard source- to-target model. This model is made pos- sible by an exhaustive candidate genera- tion strategy specifically enabled by the features of the **portmanteau** task. Ex- periments find our approach superior to a state-of-the-art FST-based baseline with respect to ground truth accuracy and hu- man evaluation.

The present paper contributes to this literature by considering **portmanteau** tests for linearity of stationary time series based on ‘generalized correlations’ of residuals from a finite-parameter linear model, that is to say autocorrelations and cross-correlations of different powers of the residuals. 1 Such tests are similar in spirit to the popular **test** proposed by McLeod and Li (1983), which is based on the empirical autocorrelations of squared residuals. The McLeod–Li **test** is known to respond well to autoregressive conditional heteroskedasticity (ARCH) but tends to lack power against many other interesting types of nonlinearity that do not have apparent ARCH structures.

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tributed as a Student with ν = 9 degrees of freedom, standardized in such a way that the variance be equal to 1. These parameters are close to those obtained when a TARCH(1,1) model (i.e. an APARCH(1,1) with δ = 1) or a GJR(1,1) model (i.e. an APARCH(1,1) with δ = 2) is fitted to daily stock indices (such as those considered in the next section). The length of the simulations is n = 4, 000, which is also a current value for daily re- turns. Table 1 displays the empirical sizes of the **portmanteau** tests at the nominal level α = 5%. If the actual level coincides with the nominal level, the empirical size over the N = 1, 000 independent replications should belong to the interval [3.6%, 6.4%] with probability 95%, and to the interval [3.2%, 6.9%] with probability 99%. Table 1 indicates that the error of first kind is well controlled (most of the rejection frequencies of the left array, and those of the line δ = 2 in the right array, are within the 99% significant limits). In term of power performance, the **portmanteau** tests are more disappointing since they fail to detect alternatives of the form δ > 2 when the null is δ = 2 (see the right array in Table 1). Other Monte Carlo experiments, not reported here, reveal that the **portmanteau** tests are much more powerful to detect wrong values of the order (p, q).

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As results from the Chow **test** (Appendix F) show, for the inventory channel, the BoE’s operational independence in May 1997 also meant a structural break in monetary policy. As already mentioned, holding oil inventories has an opportunity cost of using money to buy oil which goes into storage and is not immediately burnt instead of investing the amount needed at the risk-free rate. The day when operational independence was officially given to the BoE is considered as a positive move towards better transparency, since interest rates set by government were often questioned. As outlined by Mihov and Sibert (2006) in his investigation on whether a shift to instrument independence affects central bank behaviour when already operating towards an inflation targeting goal, the greater autonomy of the BoE has played an important role. His estimations show that during the period after obtaining operating independence, the response of the BoE to inflationary pressures ultimately increased with anchored inflation through the output gap. Therefore, it can be assumed that a higher level of transparency and credibility helped to anchor inflation expectations as well as expectations about future developments in interest rates. Thus, in relation to the model of transmission mechanism, results from the Chow **test** (Appendix F), also confirm these results since the null hypothesis of no structural break can be rejected, for stability the models for the UK inventory channel (1.430>0.2312), OECDEU inventory channel (1.2455>0.298) as well as for OECD inventory channel (1.331>0.265), lead to the necessity of splitting the period into the pre- and after-independence periods. Different results can be observed from the Chow **test** for the supply channel. In the case of the supply channel, the null hypothesis can be rejected only in the case of the OPEC oil supply (0.712>0.587) and world oil supply (0.886>0.477), while the rest of the models show no structural break on this date.

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Peña and Rodríguez (2002) introduced a **portmanteau** **test** for time series which turns out to be more powerful than those proposed by Ljung and Box (1986) and Monti (1994), and approximated its distribution by means of a two-parameter gamma random variable. A polynomially adjusted beta approximation is proposed in this paper. This approximant is based on the moments of the statistic, which can be estimated by simulation or determined by symbolic computations or numerical integration. Various types of time series processes such as AR (1) , MA (1) , ARMA (2,2) are being considered. The proposed approximation turns out to be nearly exact.

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The problem of testing for neglected nonlinearity in time series models has attracted a great deal of interest in recent years. A multitude of statistical procedures designed to **test** the null hypothesis of linearity against nonlinear alternatives are available in the literature, including general **portmanteau** tests without a specific alternative as well as tests with fully specified parametric alternatives; Tong (1990) and Teräsvirta, Tjøstheim, and Granger (2010) provide useful overviews. Linearity tests have become an essential first step in model-building exercises since, due to the diﬃculties associated with the statistical analysis of nonlinear models, it is often desirable to establish the adequacy or otherwise of a linear data representation before exploring more complicated nonlinear structures.

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Due to the complexity of both component word selection and blending, previous **portmanteau** gen- eration systems have several limitations. The Neho- vah system (Smith et al., 2014) combines words only at exact grapheme matches, making the generation of more complex phonetic blends like “frenemy” or “brunch” impossible. ¨Ozbal and Strappavara (2012) blend words phonetically and allow inexact matches but rely on encoded human knowledge, such as sets of similar phonemes and semantically related words. Both systems are rule-based, rather than data-driven, and do not train or **test** their systems with real-world portmanteaux.