In my humble opinion, if your intention is to analyse the rate to identify any significant change, then do just that. There's no need for "sliding windows", spectral analysis, polynomial curve-fitting or anything else. For example, calculate the rate from the start year to a succession of years, e.g. 1900-1910, 1900-1911, and so on to the last year of data. I've made it a standard analysis in almost all of my spreadsheets, and shown examples in a number of posts. While the amount of variation in the long-term rate reduces with the data length, significant year-to-year changes are still clearly represented in addition to longer-period change. Here's the chart for Sydney - I've used a 121-month (10-year) centred running mean. The rate has increased a little from the previous chart's 0.89 mm/year (to 2010).
|Sydney, NSW - Sea level 1914-2012 (Data source: BOM)|
The plot of the annual rate shows a break in slope at 1997, and a small increase thereafter.
|Sydney, NSW - trend in mm/year from date on lower axis.|
Fremantle has seen a definite change after 1994 - the running mean shows an uptick after then. This is not surprising, all West and North-West Australia stations show similar upticks, an acceleration in fact; in the Fremantle case after around 40 years of little change, even a slight reduction after the middle 70's.
|Fremantle. WA - Sea-level 1897-2012 (Data source: BOM)|
The long-term trend plot reflects the change, with a break in slope at 1994, and an increasing upward trend after 1998.
|Fremantle. WA - trend in mm/year from date on lower axis.|
There are those who would have you believe that nothing of the sort has happened; "situation normal, no change", but the evidence is clear. More on this in a post in preparation. However, the fairly sharp increase in rate over the last couple of decades around the west of Oz and the far-western Pacific in general is matched by virtually no change on the eastern shores - North and South America, and little or no change in the central Pacific. It's quite clear to me that what the satellites have recorded over the last 20 years is fairly accurate - those who would have you believe otherwise never actually compare tide-gauge data for exactly the same period as the satellite timespan. If you've seen such claims, check out what was actually compared - nothing, just a few longer-term charts produced. "See, there's no comparison!" they say, when they've done no comparison whatsoever. More (in detail, with real comparisons) on that in a future post too.