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As a working alternative to my "tired old eyes" what I would do is as follows. Statistics longa, Eyesight brevis . I took the 9 annual values for Coventry and obtained and with stats here I would …

The moving-average approach A.K.A. arima modelling can be used to compute the probability that the most recent values is statistically significantly different from expectations. Simply take the observ …

https://stats.stackexchange.com/search?q=user%3A3382+daily+sales+data will give you a number of discussions regarding predicting daily data and subsequentally month end totals . The issue is you need …

Only the data knows for sure ! with apologies to Lamont Cranston . One would have to capture any ARIMA structure to be able to "SEE" other significant phenomenon like Pulses , Level Shifts, Seasonal …

Well John you might be at risk using a single trend model. If your data has a level shift you may be falsely concluding about a persistent change over time. … If your data is more representative of y(t)=y(t-1) + constant your trend model doesn't apply. I could go on for days about how trend models of the form y(t)=a+b*t are inadequate but I won't (here !). …

Early work did not include Trend Detection but more recent software advances does so. … Particularly Detecting initial trend or outliers might be illuminating …

It is interesting (at least to me) that at period 27 (1975) the trend abated while the error variance reduced. …

In order to detect the periods that deviate from the trend one has to detect the trend in such a way that any existing deviations do not distort the identification of the trend. … In order to answer your question , I need to define "trend" and "deviate from trend ... anomaly" The general definition of what a trend is : The general course or prevailing tendency” From http:// …

Simply build an ARIMA MODEL that separate signal from noise incorporating any identifiable deterministic structure such as changes in levels/trends/seaonal pulses/parameter or variance change over tim …

Since you have unequal intervals between readings time series methods are inapplicable. BUT I would consider using an average reading for a fixed interval of time say 60 second intervals and build/ide …

Look at Trend shifts in timeseries and pick up some pointers. … Detecting trend is not accomplished by specifying a model or a derivative but by allowing the data to suggest the underlying model and then drawing inference. …

You ask "But what if I want to understand and explain the forces underlying trend? I want to look for the reasons for the increase and then the eventual reversal in the trend and subsequent decline." … in trend. …

It does not appear to have non-linear trend effects just a response to unspecified predictor series. There may also be short term arima effects. Only your data knows for sure ! …

De-trending requires a pre-specification of of how many values do you require before declaring that a new trend has started. … Outliers and ARIMA structure in a time series can lead to distortions in the identification of trend-point changes and may need to be incorporated prior to trend-point detection. …

Sarah, Take your 36 numbers (12 values per cycle ; 3 cycles ) and construct a regression model with 11 indicators reflecting possible week-of-the-semester effect and then identify any necessary Interv …