and are called jointly wide-sense stationary if they are both wide-sense stationary and their cross-covariance function depends only on the time difference . This may be summarized as follows: Relation between types of stationarity If a stochastic process is N-th-order stationary, then it is also M-th-order stationary for all . If a stochastic process is second order stationary () and has finite second moments, then it is also wide-sense stationary. If a stochastic process is wide-sense stationary, it is not necessarily second-order stationary. If a stochastic process is strict-sense stationary and has finite second moments, it is wide-sense stationary. If two stochastic processes are jointly (M + N)-th-order stationary, this does not guarantee that the individual processes are M-th- respectively N-th-order stationary. Other terminology The terminology used for types of stationarity other than strict stationarity can be rather mixed. Some examples follow. Priestley uses stationary up to order m if conditions similar to those given here for wide sense stationarity apply relating to moments up to order m. Thus wide sense stationarity would be equivalent to "stationary to order 2", which is different from the definition of second-order stationarity given here. Honarkhah and Caers also use the assumption of stationarity in the context of multiple-point geostatistics, where higher n-point statistics are assumed to be stationary in the spatial domain. Tahmasebi and Sahimi have presented an adaptive Shannon-based methodology that can be used for modeling of any non-stationary systems. Differencing One way to make some time series stationary is to compute the differences between consecutive observations. This is known as differencing. Differencing can help stabilize the mean of a time series by removing changes in the level of a time series, and so eliminating trends. This can also remove seasonality, if differences are taken appropriately (e.g. differencing observations 1 year apart to remove year-lo). Transformations such as logarithms can help to stabilize the variance of a time series. One of the ways for identifying non-stationary times series is the ACF plot. Sometimes, seasonal patterns will be more visible in the ACF plot than in the original time series; however, this is not always the case. Nonstationary time series can look stationary Another approach to identifying non-stationarity is to look at the Laplace transform of a series, which will identify both exponential trends and sinusoidal seasonality (complex exponential trends). Related techniques from signal analysis such as the wavelet transform and Fourier transform