Various linear models may be specified when attempting to estimate an apparent linear trend in real data sets, based on assumptions about the possibly unknown mechanism for generating the data. However, in many cases the best-fit line obtained from implementation of the specified model does not agree at all with the apparent trend in a scatterplot of the data, based on the evident geometric str...

Climate studies often fit linear trends to data. In many cases simplifying assumptions such as independent errors and constant variance are used. We review a variety of approaches to estimating linear trends, and illustrate with US temperature data how oversimplified assumptions may lead to false significance. We outline a variety of methods to fit nonlinear trend models. Using the Berkeley Ear...

In examining a plot of a time series of a scalar climate variable for indications of climate change, we might pick out what appears to be a linear trend commencing near the end of the record. We demonstrate that visual determination of the starting time of the trend can lead us to incorrectly declare a trend to be significant when we base our assessment on standard linear regression analysis; i...

Global surface temperature anomalies post-1958 are examined for evidence of significant trends. The routine application of a linear least-squares method is critiqued. Testing for model misspecification in the form of serial correlation and heteroskedasticity in the residuals leads to consideration of a piecewise trend with lagged anomalies and a linear model of the error variance. While the naï...

Each time-series has its own linear trend, the directionality of a timeseries, and removing the linear trend is crucial to get the more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to a huge number of possible subsequences. In this paper we define this problem the linear detrending subsequence matching and propose its efficien...

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed l1 trend filtering method substitutes a sum of absolute values (i.e., an l1-norm) for the sum of squares used in H-P filtering to penalize variations in the estimated ...

In this paper trends of precipitation and stream flow are analyzed in the Atrak River basin in the North Khorasan province. Normal score linear regression, Mann-Kendall, and Seasonal Kendall trend tests were adopted. Three precipitation variables and two stream flow variables including total precipitation, maximum daily precipitation, and number of rainy days, mean discharge and peak discharge ...

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick–Prescott (H-P) filtering, a widely used method for trend estimation. The proposed !1 trend filtering method substitutes a sum of absolute values (i.e., !1 norm) for the sum of squares used in H-P filtering to penalize variations in the estimated tre...

We analyzed the influence of cytology development to frequency of precancerosa (Cervical intraepithelial neoplasia grade 3 - CIN 3) and cervical cancer. The number of examined Pap smears increased significantly in the analyzed period. The calculated linear trend shows an average four-year increase of 17,283.35 smears. The number of detected CIN 3 increased accordingly. The calculated linear tre...