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STAT30010 Time Series Analysis Assignment Example UCD Ireland

This course provides an opportunity for students to learn some basic techniques in Time Series Analysis. A Time series is a set of measurements taken at regular intervals over the course of time. This course provides an opportunity for students to learn some basic techniques of this subject, with examples coming mostly from economics but also extending into finance econometrics (CPI) inflation, GNP, GDP, etcetera.

Time series goes beyond just equity prices or oil prices – they can be found across many disciplines like astronomy where we use them to predict past weather patterns using seasonal cycles, or meteorology where we use them to predict the weather a few weeks in advance. The beauty of time series is that they can help us understand past behavior and make predictions about future trends.  Topics covered include, among others: Stationarity, ARIMA models, Parameter Estimation, Forecasting, and Cointegration. Additional topics may be included which may vary from year to year.

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In this course, there are many types of assignments given to students like individual assignments, group-based assignments, reports, case studies, final year projects, skills demonstrations, learner records, and other solutions are given by us.

Upon completion of this module students will be able to:

Assignment Activity 1: Identify the stationarity properties of a time series:

The stationarity property of a time series is its levelness over time, in other words, it cannot show trends. This could also mean that the variance in the data does not change over time (constant variability).

Stationarity implies that observed or calculated data should be steady across time or remain constant. The dataset can be examined without having to take into consideration when the measurement was taken. It’s also characterized by no long-term changing trends in observed/calculated data; constant variance.

A stationary process (or state) is one whose statistical properties like its mean and autocovariance function are independent of time; thus, they do not vary with “t”. A stochastic process may or may not be stationary.

There are three types of stationarity:

  1. Temporal Stationarity: A process is temporally stationary if the mean and variance are constant over time.
  2. Spatial Stationarity: A process is spatially stationary if the mean and covariance are constant over space.
  3. Homogeneity: A process is homogeneous if the mean and variance are constant along with parallel shifts in time or space.

Assignment Activity 2: Model the time series using Box-Jenkins ARIMA techniques:

The Box-Jenkins method is a time series forecasting technique. It is a classic statistical approach to modeling and smoothing time series. In the ARIMA methodology, prediction of future values of a time series can be carried out by fitting an autoregressive or moving average process to the observed data, as differentiated from other techniques such as regression analysis that refer to the relationship between variables. ARIMA modeling is typically used when there is one or more than one autocorrelation present in the data set.

Box-Jenkins methodology refers to a time series model developed by George Box and G.M Jenkins. These models are widely used for forecasting future values based on historical information.

The ARIMA model is made up of three components:

  1. The first component is the autoregressive (AR) part, which captures the short-term dynamics of the series.
  2. The second component is the Moving Average (MA), which captures the long-term dynamics of the series.
  3. The third component, the differencing, converts a non-stationary time series into a stationary one.

The Box-Jenkins approach is to identify the main underlying factors that are driving the dynamics of the time series and to use these factors in an econometric model that explains how they impact your outcome.

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Assignment Activity 3: Estimate parameters for ARIMA models using a variety of procedures:

Parameter estimation is the process of identifying the specific coefficients in a model that best fit the observed data. There are a variety of methods to estimate ARIMA model parameters, including:

  1. Least squares or Maximum likelihood (ML) estimation: This is the most commonly used method and it involves minimizing the sum of the squared errors between the model forecast and the actual data.
  2. Akaike Information Criterion (AIC): This estimator uses a measure of goodness of fit between the estimated model and the actual data to pick the best fitting model for time series forecasting. This method is preferred when there are many possible models that could be applied to your time-series dataset, as it helps to weed out the weaker models.
  3. Bayesian estimation: This method uses a prior distribution on the model parameters and then calculates the posterior distribution by incorporating the data. This approach is particularly useful when you have little information about the parameters of your model, as it allows you to incorporate all of the data in order to estimate them.
  4. Geweke’s Delta Method: This method involves constructing a simulated time series by first estimating ARIMA parameters and then generating a new time series from the estimated model. Comparing this simulated new time series with the observed original one can help estimate the goodness of fit between them.

Assignment Activity 4: Produce forecasts for a given time series:

Forecasting is the process of predicting future values based on past and current data. Once you have estimated the parameters for your ARIMA model, you can use them to generate forecasts for future values of the time series. There are a variety of methods for doing this, including:

  1. Point forecasts: This is simply predicting the next point in the time series.
  2. Interpolation: This involves predicting values between the known points in the time series.
  3. Extrapolation: This is predicting future values beyond the end of the observed data set.
  4. Seasonal adjustment: This adjusts your forecasts to take into account regular seasonal patterns in the data.

Assignment Activity 5: Be familiar with additional topics such as cointegration, vector autoregressive models:

There are a number of additional topics that you should be familiar with if you are working with time-series data, including:

  1. Cointegration: This is the phenomenon where two or more time series are integrated (i.e. they have a unit root) but are nevertheless related to each other. This can be exploited in econometric models in order to improve the accuracy of the predictions.
  2. Vector autoregressive (VAR) models: This is a model that allows you to include more than one time series in your analysis. This can be particularly useful when you want to understand how different time series are related to each other.
  3. Time-series decomposition: This is the process of breaking down a time series into a trend, seasonal and residual components. This process can be useful for interpreting your time series results.

These are the main activities you would need to perform in order to become familiar with working with time-series data. The specific tasks will depend on the dataset that you are given, but this is a general outline of what you should try to accomplish.

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