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# Analysis of Time Series Dataset PDF

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Table of ContentsINTRODUCTION...........................................................................................................................3Task 1...............................................................................................................................................31. Creation of time series dataset to calculate aggregate consumption function.........................3Anticipations...............................................................................................................................4Serial correlation.........................................................................................................................4Stationarity..................................................................................................................................5Estimating an aggregate consumption function..........................................................................8Task 2.............................................................................................................................................101 Analysis of time series dataset and survey of consumer finances.........................................10Logarithmic model....................................................................................................................12Debt-to-income ratio.................................................................................................................14Gender-specific regressions or dummy variables.....................................................................15Main specification.....................................................................................................................17Diagnostic checks......................................................................................................................17Including extra variables and interaction terms........................................................................18CONCLUSION..............................................................................................................................19Appendix........................................................................................................................................20Do-file for Task 1......................................................................................................................20Do-file for Task 2......................................................................................................................22
INTRODUCTIONTime series dataset refers to data points which are graphed with respect to time. Itbasically includes series taken at consecutive distributed points in time. Therefore, it is asuccession of discrete-time data. Consumption function refers to functional relationship betweengross national income and total consumption (Anselin, 2013). This report deals with creation oftime series dataset so that overall consumption function can be evaluated. Furthermore, synthesisof time series dataset is done and also analysis of dataset which is based on survey of finances ofconsumers is provided.Task 11. Creation of time series dataset to calculate aggregate consumption function.Time series dataset refers to quantity that represent values which are taken by variable orentity in certain time like year, quarter or month. This series occur when same standards arecanned on regular basis. Consumption function is defined as a economic formula which is usedto correspond relationship between overall consumption and gross national income.In this report, country which is chosen is Australia. This report contains data which havebeen used derived from Eurostat database. It is a database with around 4600 datasets whichcomprises of approx 1.2 billion statistical data values. Eurostat is considered as exploit ofstatistical collection of information. It contains data of every quarter for minimal grossexpendable income for household sector, their terminal consumption disbursement of householdsand price index which was 2013=200 Data is obtained from Eurostat database which isaccessible at million units of currency. Therefore, consumer price index is used which isavailable on OECD website of Australia. In that house price index which was obtained fromEurostat for 2013=200. It is not similar to inflation but it is approximate value which has beenused for creation of dataset in real conditions (Anselin, Florax and Rey, 2013). There is no data available with respect to Australia; therefore data which is utilized isfluctuated across quarters. House price index (hpi) refers to measurements of fluctuation inprices of residential houses in a form of percentage change from particular start date. For thisrepeat-sales regression, simple moving average and hedonic regression can be used forcalculations. It will function as proxy for wealth which is on based two variables which will be
used in regression. After this alterations are made with usage of Microsoft Excel and then thisfile has been exported to Stata. In this time dimensions were fixed and different entities wererenamed. Furthermore, Moodle is used for assessment.AnticipationsSome assumptions were taken for time series regression, so that unbiased estimators canbe calculatedstochastic process which relates with linearity in parameters; {(xt1, xt2, ..., xtk, yt) where t varies from 1 to n and follows linear model whichincludes value from yt = O0 + O1xt1 + ...+ Okxtk + ut where range of t in ut is between 1 to nwhich denotes errors (this includes sequence of periods, different parameters) and k is a variable.Independent variables are not constant as well as they are not perfect linear accumulationof other independent variables which are present in sample which means that there is noperfect co linearity.Accepted value of error ut is zero for every t’s value, such that E(ut|X) = 0), where Erepresents explanatory variables and value of t lies in between 1 to n.Ordinary least squares (OLS) value will be similar to true parameters, when theseassumptions or anticipations are taken into consideration. This is known as theorem ofunbiasedness of OLS for particular time series regressions.Serial correlationIn context of cross-section regression, vital anticipation which was taken considers thatdifferent observations on e and y are not related with each other that is cov (yt, ys) = cov (et, es)=0 for t s where t and s refer to different time periods (Asteriou and Hall, 2015). In this s and tdenotes unlike time periods. But as per our considerations, these anticipations will be doubtful tocling to. Wealth, income and consumption expenditure which are interrelated as they changesteadily and not rapidly, these values will be dependent on previous values which were obtainedat another time period this means that they are correlated.
Figure 1 Autocorrelation of disposable income and expenditure consumption for ten differentlags.In above figure, in both the cases for initial four autocorrelations are distinct from zero with 5%level. When data is tested using Stata for autocorrelation then outcome obtained is clearer as itcan be seen in above figure. When taken into consideration, then it shows that disposable incomeis dependent on previous disposable income (Brooks, 2019). These outcomes follow anticipationfor theorem of unbiasedness of OLS estimators for time series regression. It is not reliable todepend on variance formula for estimator.StationarityAnticipation is desecrated in dataset, therefore this section is taken into consideration.From graphical representation it is clear that disposable income and consumption expenditurewill grow with time. Graphical representation will be in upward direction as it is alreadymentioned above that Eurostat dataset is not adjusted seasonally rather than it is across quarter.
Figure 2 Household consumption expenditure and real gross disposable household income overmillion units of Polish zloty.Time series regression depends on anticipation that variables which are under consideration arestationary. A time series yt is stationary that means that mean and variance are stable within timeand covariance of two values of series is only dependent on time length which separates twovalues and they are not dependent on variables at exact time (Elhorst, 2014).As per Dickey-Fuller test which is for unit root test for null hypothesis has a unit root whichindicates that variables are non-stationary. Null hypothesis must be considered at reasonablelevels when test is conducted for household consumption expenditure and disposable income.For this non-stationary objects are taken into account. Unit root null hypothesis will beconsidered for house price index.

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