Ljung-Box 53.263 31.41 7.4353e-05 From this output, we can read that analyzing the growth with 20 lags and at 5% significance level, we reject H0 of no autocorrelation. This result leads us to think that this data can be a great source for AR or ARMA dynamic models for predicting future GDP levels. 2. ARMA Model for GDP Growth a. Estimation of ARMA Model From the conclusions drawn in 1.b, we decided to first model the GDP growth using an ARMA (1, 2). The model estimate is based on Maximum Likelihood estimation since we can observe sporadic spikes in the variability of the GDP growth over time as seen in figure 1.b. In fact, with MLE we are able to arrive to robust inference as under The OLS estimator which is identical to the maximum likelihood estimator (MLE) under the normality assumption for the error terms. The estimation equation is as follows: (eq 1.1) The MLE results are as follows: ARMAout = Estimate RobustSE tStat Intercept 0.0029952 0.0011664 2.5678 AR1 0.31523 0.19208 1.6411 MA1 0.11393 0.18108 0.62917 MA2 0.14936 0.12037 1.2409 logL 500.77 NaN AIC -10.197 NaN NaN BIC -10.111 NaN NaN We assessed the significance of each coefficient using the t critical value of 1.9778 for a two tailed distribution with 134 degrees of freedom (135…
In the example provided in the textbook, one is waiting for a bus going from Chicago to New York when he is approached by a man in a Chicago Bears hat. This man politely asks for the victim’s wallet while subtly presenting a gun. Generally, most people would hand over the wallet without hesitation. Why? There are several facets and estimator variables at play here. In this specific scenario, the mere stress and anxiety provoked by such an encounter and the presentation of a deadly weapon are…
One such alternative include minimizing the summation of errors in absolute quantities. According to Sykes, unbiasedness is when a parameter’s true value equals the mean of probability distribution. He states that consistency is comparison of different estimators that are unbiased and finding the lowest variance. He also defines consistency as generation of accurate estimates by taking advantage of extra data. The difference in interpretation of coefficient estimates is that multiple regression…
or imperfect knowledge of enemy capabilities. In calculating the costs and benefits of war, a clear and certain understanding of the opponents’ capabilities will affect the state’s decision significantly. Cognitive biases and heuristics fall under three main categories – simplicity, consistency, and poor estimators. National leaders must be able to justify foreign policy actions and responses to other states’ actions to constituents. Explaining such complex scenarios and actions often poses a…
Linear Trend Line: A trend line, often referred to, as a line of best fit, is a line that is used to represent the behavior of a set of data to determine if there is a certain pattern. Curvilinear Trend/Regression: The relation between variables when the regression equation is nonlinear (quadratic or higher order) Mean Absolute Deviation (MAD): set of data that is the average distance between each data value and the mean. The average absolute forecast error. Mean Squared Error (MSE):…
superiority. This essay is going to make an appraisal of the social identity theory by weighting up the strengths and limitations of social identity theory with reference to relevant studies, however, the main study will be discussed is by Tajfel in 1970. Tajfel aimed to investigate if boys placed in random groups based on an arbitrary task would display in-group favouritism and inter-group discrimination. There were 64 schoolboys aged 14 to 15 participated in the experiment. They were in…
studies that aim to establish causal relationships face several methodological challenges. The first of these challenges is lack of the counterfactuals. As there are no baseline data in many observational studies and it is not possible for the treatment group to undergo and not undergo the treatment at the same time, the question “what would have happened to the treated group without the treatment” cannot be answered. Although constructing a control group can help to address this problem,…
Because some students naturally learn faster than others do, unobserved heterogeneity may bias our estimates of β, or persistence, upwards. Additionally, measuring educational achievement through testing is prone to measurement error – even if we assume that tests can quantify the presence of important traits like work ethic and emotional intelligence. Because the test scores occur as a lagged dependent variable, measurement errors lead to attenuated estimates of persistence, even under the…
relationship between elements within a time series. It can affect the variance of our estimators, and cause us to incorrectly estimate our true mean, Y ̅. To properly study and analyze a covariance stationary time series, we need to know something about the correlation/covariance structure. Several methods exist for dealing with serial correlation. Here, we will deal exclusively with batch means, replication/deletion, and the Mean Squared Error Reduction (MSER) technique. The goal of these…
register.) Children with a local GP as in their local area. The exclusion criteria are- Children who have other co morbidities as hypertension, asthma, genetic causes of obesity, family history of obesity. Children who have learning difficulties or mental health problems. Children diagnosed with diabetes before 5 years of age. (It is anticipated that the numbers will be small.) Family history of diabetes- as the association is to see if obesity causes Type 1 diabetes and not genetic causes. 3. A…