In order to compare the land N hemisphere temperature anomaly with a random walk I generated 1560 random numbers that fit a normal distribution with σ = 0.36 and summed them using,
Σ 0 = δ 0 Σ k = 0.5 Σ k-1 + δ k k>0
Then the result was summed over a period of 60 "months" to produce a five "year" average. The result for the random walk is shown in the following plot.
There are fluctuations present in the random walk and short linear segments but they are not as pronounced as the temperature anomaly data. Clearly something other than a random walk is also happening in the temperature anomaly data.