Lunga memoria, persistenza, trend e mean reversion delle serie temporali dei prezzi dell'acqua. Serie temporali dei prezzi dell'acqua

The purpose of this thesis is to study water prices time series across five regions through fractional integrated methods of detecting long-memory. The five regions are: Asia Pacific & Russia, Europe, USA, Latin America and the general globe. The understanding sought is that of long memory behaviour of water prices, with either business days or weekdays being the frequency of the data from January 2010 to January 2020 for four of the regions save the Latin America data set that only has prices from March 2019 to January 2020. The data were obtained from the Thomson Reuters Eikon database which a financial information service, that broadly has data on companies, financials markets, news,countries’ economies, analytics and trading tools. Tests employed are: two parametric Robinsons’ tests with the first havingassumptions of residuals with autocorrelation , and second the assumption of noautocorrelation on residuals, the semi-parametric Robinson tests based on Whittle approximation and finally the non-parametric Lo’s modified R/S statistic. Parameters that will be estimated are the differencing d or the self similarity H. Particularly Lo’s modified R/S by analysis estimates the self-similarity parameter H of the time series which unfortunately being easier to calculate has the caveat of being biased in favor of accepting the null hypothesis of no long memory. The Local Whittle likelihood test selects the parameter which maximizes an approximate form of frequency domain Gaussian likelihood calculated in an neighborhood of the zero frequency. The results depend on the selection of the parameter that defines the width of the neighborhood, making them not always clear. The results indicate that there is a high degree of persistence as the values of d the differencing parameter are close to one in all regions and even higher in the the uncorrelated errors assumption of Robinson tests. Under the assumption of autocorrelated errors, there are small tendencies in mean reversion in practically all regions with the exception of Latin America. Structural breaks are investigated and there are multiple breaks in the data: five for Asia Pacific & Russia and Global data, four in both the USA and Europe and finally three in Latin America. There is however no significant change in the degree of persistence from the subsamples and mean reversion is found once autocorrelation is allowed.