Using the series given in the "Project Pt3.txt" file,

(a) Make a time series plot and comment on the stationarity of the series. If you see signs of nonstation- arity, take differences and plot the resulting series until you see no evidence against stationarity.
(b) Specify the model, write down your model, and estimate the parameters of the model via maximum likelihood.
(c) Carry out a full residual analysis and comment on the adequacy of your model assumptions.
(d) Overfit two other models to this series and describe what the results tell you about the adequacy of the model you chose.

ProjectPt3.txt :

"x"
"1" 0
"2" 3.99202666297506
"3" 3.41859682261657
"4" -3.09554192630901
"5" -8.66073023285051
"6" -10.9471996389833
"7" -11.8649645157883
"8" -12.9087168265868
"9" -13.7830841033954
"10" -13.7087114670453
"11" -11.4063190563769
"12" -8.97210912221096
"13" -7.1188928892723
"14" -6.84041384538536
"15" -8.10150464279881
"16" -11.3005321299622
"17" -13.4113446179925
"18" -10.7872803849601
"19" -7.44998637289548
"20" -4.98992176918874
"21" -4.86836631900933
"22" -6.71226374424198
"23" -13.0533221970498
"24" -21.1731334929813
"25" -25.7119520306314
"26" -26.5372218599308
"27" -24.3776629817097
"28" -24.2103065286461
"29" -24.8166280327539
"30" -26.1662039055795
"31" -28.7149050112558
"32" -29.2384900281232
"33" -29.8631753073185
"34" -32.6511553582221
"35" -31.8454545258475
"36" -23.692041315002
"37" -18.380259319043
"38" -21.9789911436425
"39" -29.3089255076588
"40" -34.6377706889206
"41" -33.2475592236949
"42" -28.519374863782
"43" -20.9544218751851
"44" -16.0106152304891
"45" -15.2487300627681
"46" -19.2871853763597
"47" -23.9320148593912
"48" -26.1194879533806
"49" -22.3992825789431
"50" -17.4608004606965
"51" -15.0166344509149
"52" -18.8183353175725
"53" -24.1445232941476
"54" -23.7560172575864
"55" -22.5135771978517
"56" -21.8047204834082
"57" -26.0999169908052
"58" -30.6083652956213
"59" -29.1264216246271
"60" -25.4858706468103
"61" -21.9712454961028
"62" -19.0040958860218
"63" -19.2565082642796
"64" -23.1340112014326
"65" -24.7154022490095
"66" -26.7029590181411
"67" -29.3323565236397
"68" -31.1367946309805
"69" -29.4117215481355
"70" -25.1004487525782
"71" -22.1934879068624
"72" -21.9613144071253
"73" -24.2560641205118
"74" -26.5270771616278
"75" -29.9471016824321
"76" -34.1992628321068
"77" -38.1256449074395
"78" -38.4841591417501
"79" -35.7138609335098
"80" -33.1579594225397
"81" -30.6598774268249
"82" -28.5963182467163
"83" -29.4662634890585
"84" -34.1116442793481
"85" -37.4480870906674
"86" -38.8938633572907
"87" -34.4814964703014
"88" -30.9940179870352
"89" -33.1532966973572
"90" -37.7753981743957
"91" -40.1291545094449
"92" -37.211706762491
"93" -28.3170170059226
"94" -21.3513657755459
"95" -19.0614172096581
"96" -20.2822899321257
"97" -24.3009065510829
"98" -26.0866217716935
"99" -25.2696406517316
"100" -26.4461664940348
"101" -27.7817546763624
"102" -26.4578492489601
"103" -22.7217281340345
"104" -18.3489672879062
"105" -19.947139999145
"106" -23.7153863828535
"107" -25.3207880260599
"108" -26.3893979420177
"109" -23.723994671645
"110" -22.9160168986812
"111" -23.9313843697281
"112" -22.6197186499457
"113" -18.293403142205
"114" -16.9826017629681
"115" -16.9133188187905
"116" -15.8555925998769
"117" -16.9253342887053
"118" -19.3124011502092
"119" -23.3387189772606
"120" -24.7548007272306
"121" -20.3463956303773