Autocorrelation

assessed with the corresponding quarter year on year. This effect compensates the business cycles variations which are more significant for economic analysis. b. Autocorrelation and Partial Autocorrelation Functions GDP growth i. Dynamic Model GDP Growth. The autocorrelation function shows the direct correlation between the time lags while the partial autocorrelation function shows the correlation between Zt and Zt+k lags after removing the autocorrelation between Zt+1 and Zt+k-1. Consequently, the autocorrelation values showing in the PACF are lower than those in the ACF since they exclude impact of intermediate lags. The ACF and the PACF are two vital tools in defining the nature of the generating process of stochastic distributions. As shown in the table below, they can be used to determine the orders of the underlying AR, respectively MA processes. In addition, the 95% confidence bands aid in recognizing the important lags. The confidence bands are centered at zero with limits of ± 2/ with n the sample size. The confidence band is for the autocorrelations of an uncorrelated sequence or white noise. If the data is statistically independent, then its sample autocorrelation has a mean of zero and an approximate standard deviation of 1/. To determine which dynamic model better captures the autocorrelation in the time series, we follow the relation shown in table 1.1. Table 1.1: Relation between ACF/PACF and AR/MA ACF PACF AR(p) tends to 0 cut off at p MA(q) cut…

Autocorrelation is not expected to be an issue with the model, given that the it is not using time series data, and it can therefore be assumed that there is no autocorrelation present in the model. To make sure that there is no perfect collinearity present in the model, it is recommended to run a collinearity test of the model (see: Exhibit 1.1). If a variable generate a VIF (Variance Inflation Factors) value above 10.0, the model might have a collinearity problem and attempts to correct the…

3.8.2 Geary’s C Another measure of spatial autocorrelation is Geary’s C statistic which ranges from 0 to 2 where 0 signifies maximum positive spatial autocorrelation or clustering, 1 signifies no autocorrelation or randomness and 2 signifies maximum negative autocorrelation or dispersal. If the values of Geary’s C are low it indicates positive spatial autocorrelation and if the values are high it indicates negative spatial autocorrelation. The calculation is similar to Moran’s I but here the…

level facet and selects stations sitting in the same facet, until fulfilling the requirement. Considering topographical facet in the procedure of selecting neighboring stations helps to utilize the dependency of precipitation on topographical features (Daly et al., 1994). The whole algorithm was implemented in cython (www.cython.org) with Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/). 4.6 Calculation of regional level climate characteristics Regional mean value of each climatic…

Specifically, I run an OLS regression with robust standard errors on excel using an add-on created by Humberto Barreto and Frank M. Howland from Wabash College. Their add-on relies on a heteroscedasticity-consistent covariance matrix to create robust standard errors. By using their add-on, I can be sure that my errors are robust and that my regression results are accurate. Running a regression with their add-on yields the same regression results as for equations 1,2, and 3. This indicates that…

the model, we have that a one unit change in the market risk premium, all other things held equal, would translate in a 1.29 increase in the SPG risk premium, concluding to be a significant change by testing the coefficient significance through the t column. On the other side, the constant term tells us that the stock is overpriced, but we can not conclude it is significant in our model because we can’t reject the not significant test with it’s t. Furthermore, after testing for serial…

frequency measure to calculate an index, called Brain function index (BFI), and used to quantify depth of anesthesia. As EEG derived features characterize different aspects of EEG signal, it would be logical to utilize multiple features to evaluate the effect of anesthetic. Toktam et al. [52], designed more robust index, a beneficial Electroencephalogram signal preprocessing method was proposed. Additionally, an efficient method was proposed to estimate the depth index during the surgery. In the…

discussion, we found that TGARCH-M model satisfied the stationary as well as the non-negativity conditions of parameters. It also captured the leverage/ asymmetric effect of the data. Irrespective of the subset of the data TGARCH-M model with t-distribution provided the better results. The best fit model for all subset of data was reported in Table 5.7 along with the diagnostic tests which showed that TGARCH-M with t-distribution satisfied the non-explosiveness condition, better capture the…

minimum mean square estimate (MMSE) of the coefficients within the EnKF algorithm. Without loss of generality, let us consider a first-order wide-sense stationary autoregressive state equation given by egin{equation} x_n = a x_{n-1} + u_n label{firstOrder} end{equation} where $a$ is a constant coefficient. The MMSE estimate of $a$ is given by ${hat a}=frac{{cal R}_x(1)}{{cal R}_x(0)}$ where ${cal R}_x(m)$ is the autocorrelation of $x$ of lag $m$. The sample MMSE estimate of $a$ can be…

the dependent variable, and the independent variables are Household size(HS), Household income(HI), Household education Index(HEI), Price(P),Total Awareness score on oil(TAS) and the Ratio of Total oil expenditure to Total food expenditure (R) .θ is the disturbance term, α is the intercept term and a, b, c, d, e and f are the corresponding coefficients of the independent variables. Based on the survey data obtained from 360 respondents a regression model is constructed. Ordinary Least Square…