Case Study 1- Construction Materials
In a Company of construction materials you want to analyse prospective preventive behaviour of a set of indicators of the production process Tile bilayers in order to identify historical trends and possible outcomes over the next productive periods.
To test if the data is a time series or not, we have used Statgraphics Centurion XV, on which I used the option Descriptive Time Series method, which gives possibility to apply the following analysis:
The Randomness tests show the results of additional tests performed to determine whether or not the time series is purely random: Three tests:
1. Runs above and below the median, calculates the number of times the series goes above or below the median.
2. Runs up and down: calculates the number of times the seesaw series. This number is compared with the expected value for a random time series.
3. Box-Pierce test: building a statistical test based on the first k sample autocorrelations to calculate.
The three tests used to determine if a data set is a random sequence of numbers, or not. Since all three tests are sensitive to different types of deviations from random behavior, not pass either suggests that the time series could not be completely random.
Partial Autocorrelation Function plot sample partial autocorrelations and the limits of probability. If the rods which extend beyond the upper or lower limits correspond to significant partial autocorrelations. That is, to see if the list of values can be treated as a number one coefficient must exceed the dotted line graph and accept a data stream that is being analysed.
The Integrated Periodogram shows the cumulative sums of periodogram ordinates divided by the sum of the ordinates of all Fourier frequencies. It includes a diagonal line on the graph alongside Kolmogorov bands 95% and 99%. If the time series is purely random, the integrated periodogram should fall within those bands between 95% and 99% of the time.
These tests were conducted in four selected indicators of Tile production.
This procedure constructs various statistics and plots for Marmolina. The data cover 15 time periods. Select the desired tables and graphs using the buttons on the analysis toolbar.
Tests for Randomness of Marmolina
(1) Runs above and below median
Median = 8,99
Number of runs above and below median = 9
Expected number of runs = 6,83333
Large sample test statistic z = 1,04103
P-value = 0,29786
(2) Runs up and down
Number of runs up and down = 9
Expected number of runs = 9,66667
Large sample test statistic z = 0,10885
P-value = 0,913316
(3) Box-Pierce Test
Test based on first 5 autocorrelations
Large sample test statistic = 2,98587
P-value = 0,702165
Three tests have been run to determine whether or not Marmolina is a random sequence of numbers. A time series of random numbers is often called white noise, since it contains equal contributions at many frequencies. The first test counts the number of times the sequence was above or below the median. The number of such runs equals 9, as compared to an expected value of 6,83333 if the sequence were random. Since the P-value for this test is greater than or equal to 0,05, we cannot reject the hypothesis that the series is random at the 95,0% or higher confidence level. The second test counts the number of times the sequence rose or fell. The number of such runs equals 9, as compared to an expected value of 9,66667 if the sequence were random. Since the P-value for this test is greater than or equal to 0,05, we cannot reject the hypothesis that the series is random at the 95,0% or higher confidence level. The third test is based on the sum of squares of the first 24 autocorrelation coefficients. Since the P-value for this test is greater than or equal to 0,05, we cannot reject the hypothesis that the series is random at the 95,0% or higher confidence level.
As can be seen both in the table of tests of randomness, no indicator shows fully satisfactory results, ie all data sets presented are not completely random time series. For this reason, it is concluded that the results of process does not allow the analysis of their behaviour. (just a sample of the whole study)