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A)

From the above graph, we can see that the highest value of crude steel is around 380 thousand tonnes while the lowest one is 220 thousand tonnes. We can easily say that this is a seasonality trend. In statistics, signal processing and financial mathematics, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan. Time series analysis comprises methods for analysing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to forecast future events based on known past events: to predict data points before they are measured. An example of time series forecasting in econometrics is predicting the opening price of a stock based on its past performance.

Time series data have a natural temporal ordering. This make time series analysis distinct from other common data analysis problems, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their education level, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A time series model will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility.)

Methods for time series analyses may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and recently wavelet analysis; the latter include auto-correlation and cross-correlation analysis.

For this graph, we have used spectrum analysis to figure out the trend. A cyclic trend (as mentioned in the graph) the quantity of crude steel has decreased over the period under review. In first quarter of 1992, the quantity was around 340 thousand tonnes which decreased to 240 thousand tonnes in first quarter of 2003.

B)

Autoregressive Integrated Moving Average (ARIMA) model was introduced by Box and Jenkins (hence also known as Box-Jenkins model) in 1960s for forecasting a variable. An effort is made in this paper to develop an ARIMA model for Total houses sold per quarter and to apply the same in forecasting Total houses sold for the three leading years. ARIMA method is an extrapolation method for forecasting and, like any other such method, it requires only the historical time series data on the variable under forecasting (Abry, 1994). Among the extrapolation methods, this is one of the most sophisticated methods, for it incorporates the features of all such methods, does not require the investigator to ...
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