I downloadeded the data for "all" and used dput(z_eth) for the z_eth from your code to create a reprex. I highly recommend a reprex when asking for help rather than giving a link to the data source.
The report for the ETS model is (M, N, N) with alpha = 0.9999 which is essentially a random walk (0.9999 is VERY close to 1) with no trend or seasonality. The best forecast for next month is the value for this month, and the best forecast two months ahead is also the value for this month, and so on.
BTW, you cannot specify an ETS model with "N" for the error.
suppressPackageStartupMessages(library(fpp3))
z_eth <- structure(list(Date = structure(c(16648, 16679, 16709, 16740,
16770, 16801, 16832, 16861, 16892, 16922, 16953, 16983, 17014,
17045, 17075, 17106, 17136, 17167, 17198, 17226, 17257, 17287,
17318, 17348, 17379, 17410, 17440, 17471, 17501, 17532, 17563,
17591, 17622, 17652, 17683, 17713, 17744, 17775, 17805, 17836,
17866, 17897, 17928, 17956, 17987, 18017, 18048, 18078, 18109,
18140, 18170, 18201, 18231, 18262, 18293, 18322, 18353, 18383,
18414, 18444, 18475, 18506, 18536, 18567, 18597, 18628, 18659,
18687, 18718, 18748, 18779, 18809), class = c("yearmonth", "vctrs_vctr"
)), avgPM = c(1.23852533333333, 0.9886999, 0.658164483870968,
0.9298494, 0.884815612903226, 1.52380051612903, 4.56761544827586,
11.1117932258065, 8.94574076666667, 11.2940913870968, 14.3731418333333,
11.8619731290323, 11.1576918387097, 12.5251499, 11.9651156774194,
9.97532326666667, 7.83666051612903, 10.1742568064516, 12.3853898928571,
34.7225876451613, 52.3605244333333, 123.960254451613, 300.6547521,
218.722350387097, 303.158966322581, 294.156990966667, 305.894181193548,
359.124333333333, 641.457032258064, 1113.998, 869.379892857143,
620.773193548387, 522.326833333333, 677.957947810119, 517.89819497206,
458.05772890401, 322.089121932106, 216.96889225722, 209.305132020477,
167.11591145233, 107.386815756542, 126.543917432639, 125.176889637093,
135.447403060861, 165.22808085934, 220.055176293835, 273.241196658867,
248.296865524552, 199.408394750545, 185.74948856629, 178.407611010639,
172.9819384357, 137.217722594039, 156.424866406223, 239.049834639276,
161.301471952526, 172.02663204292, 208.082405478535, 236.020492827033,
259.911378254903, 402.062691077539, 368.711580995463, 376.255336613523,
486.478629431027, 622.155608773077, 1201.59379454444, 1696.35929772083,
1732.52175932552, 2294.56742548414, 3147.8595091409, 2328.87417013744,
2141.12849792455)), row.names = c(NA, -72L), key = structure(list(
.rows = structure(list(1:72), ptype = integer(0), class = c("vctrs_list_of",
"vctrs_vctr", "list"))), row.names = c(NA, -1L), class = c("tbl_df",
"tbl", "data.frame")), index = structure("Date", ordered = TRUE), index2 = "Date", interval = structure(list(
year = 0, quarter = 0, month = 1, week = 0, day = 0, hour = 0,
minute = 0, second = 0, millisecond = 0, microsecond = 0,
nanosecond = 0, unit = 0), .regular = TRUE, class = c("interval",
"vctrs_rcrd", "vctrs_vctr")), class = c("tbl_ts", "tbl_df", "tbl",
"data.frame"))
z_eth_test <- z_eth %>% slice(1:floor(.75*nrow(z_eth)))
z_eth_out <- z_eth %>% slice((floor(.75*nrow(z_eth)):n()))
ets_mod_auto <- z_eth_test %>%
model(ets = ETS(avgPM))
ets_mod_auto %>% report()
#> Series: avgPM
#> Model: ETS(M,N,N)
#> Smoothing parameters:
#> alpha = 0.9999
#>
#> Initial states:
#> l[0]
#> 0.9869478
#>
#> sigma^2: 0.3323
#>
#> AIC AICc BIC
#> 593.5255 594.0055 599.4925
fc <- ets_mod_auto %>% forecast(h = length(z_eth_out$avgPM))
fc %>% autoplot(z_eth_test)

Created on 2021-07-16 by the reprex package (v2.0.0)