Search results
Results from the WOW.Com Content Network
The structure function determines all stochastic properties of the individual data string: for every constrained model class it determines the individual best-fitting model in the class irrespective of whether the true model is in the model class considered or not. In the classical case we talk about a set of data with a probability ...
Cochran's test, [1] named after William G. Cochran, is a one-sided upper limit variance outlier statistical test .The C test is used to decide if a single estimate of a variance (or a standard deviation) is significantly larger than a group of variances (or standard deviations) with which the single estimate is supposed to be comparable.
In many simple cases the probability density function is fully specified by and (), and () = (see Examples). It is easy to see that if F(t) is a one-to-one function and T is a sufficient statistic, then F(T) is a sufficient statistic. In particular we can multiply a sufficient statistic by a nonzero constant and get another sufficient statistic.
In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent ...
In general, any infinite series is the limit of its partial sums. For example, an analytic function is the limit of its Taylor series, within its radius of convergence. = =. This is known as the harmonic series. [6]
In regression and time-series modelling, basic forms of models make use of the assumption that the errors or disturbances u i have the same variance across all observation points. When this is not the case, the errors are said to be heteroskedastic, or to have heteroskedasticity , and this behaviour will be reflected in the residuals u ^ i ...
Consider a concrete example, such as the global surface temperature record of the past 140 years as presented by the IPCC. [3] The interannual variation is about 0.2 °C, and the trend is about 0.6 °C over 140 years, with 95% confidence limits of 0.2 °C (by coincidence, about the same value as the interannual variation). Hence, the trend is ...
Time series: random data plus trend, with best-fit line and different applied filters. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time.