# tbats() model not capturing seasonality (weekly data)

I have below 4 years of weekly data which has complex seasonality of varying seasonal length. I have assigned the first 160 data points as training and the rest as test with frequency=52. It seems tbats() ignores the seasonality and comes up with below results while running on train data . why is it ignoring the seasonality?

when I fit Arima-Fourier with k=3 Fourier terms (selected based on the lowest AIC), the results would be much better

STL() decomposition of seasonality is more supportive of Arima-fourier results

DATA: c(2336,186,1563,987,1339,2542,978,1445,367,2836,890,3434,5389,9175,4469,11045,9473,11303,9372,5668,7576,7799,4282,4995,2457,3610,5725,320,3151,6690,7795,4310,3348,5415,5106,3742,4975,5165,2866,3990,2528,3721,1054,4717,4463,903,2035,4387,1751,2682,4889,3355,3796,5223,3129,2038,1760,2591,4372,2692,6354,6836,1983,4285,4446,1507,7089,694,247,10429,6873,16891,11285,10849,6914,7917,7318,6380,7800,6125,4557,5440,4243,11141,6698,3971,852,4485,3803,3896,1717,3062,6556,2301,2859,4140,6359,3069,2268,2612,6708,5308,5233,4578,6644,6310,5211,5058,3466,7697,6223,3952,4531,7809,7999,8066,19295,23812,20138,13374,20584,15934,14939,16724,14652,11569,10164,6911,9714,13141,12362,8075,7275,5622,3817,4933,6743,5437,8102,7927,5466,9497,7343,1762,5626,5508,4230,3316,4528,3215,7884,4577,3256,6681,6499,5016,2601,2384,3404,3640,3834,2922,6199,8887,8062,5899,801,9774,7897,10485,9792,15708,14301,12490,17142,15197,17464,19602,15500,12963,16513,12490,13902,10939,11892,9058,6946,9053,5011,11090,5124,7782,6162,4921,4460,4215,9498,6833,10164,9371,7632,5866,2405,1403,8716,3521,13422,5241,7201)

2. Per the original TBATS publication (see section 3.3), the model is selected based on information criteria. In your particular case, you may simply have too much noise. Or you may have a bug in your code, because if I encode your data as a ts with frequency=52, I indeed get a seasonal forecast out of tbats: