1. Time Series. The code ts (datVec, start=c(1960,3), frequency-12) creates a time series with monthly observations (frequency=12), with first observation in March 1960 (start=c(1960o,3)) and with...

Extracted text: 1. Time Series. The code ts (datVec, start=c(1960,3), frequency-12) creates a time series with monthly observations (frequency=12), with first observation in March 1960 (start=c(1960o,3)) and with values specified in the vector datVec. Suppose z1, 22, ..., zn is a time series. Then we define the exponentially weighted moving average of this time series as follows: select a starting value mo and select a discount factor 8. Then calculate m1, m2, ..., mn recursively as follows: for t = 1, 2, ..., n et = Zt - mt-1 my = m-1 + (1– 8)e (a) Write a function tsEwma(tsDat, mo=0, delta=0.7) where tsDat is a time series, mo is the starting value mo and delta is 8. The function should return m1, m2,..., mn in the form of a time series. (b) In general, looping over named objects is much slower than looping over objects which do not have names. This principle also applies to time series: looping over a vector is much quicker than looping over a time series. Use this observation to improve the execution speed of your function which should still return a time series. Investigate the difference in speed between the functions in parts (a) and (b) by using the function system.time. (o) Write a fungtion colled which tol mante the following