Model families: TimesFM, Chronos/Chronos-Bolt, Moirai/Moirai-MoE, MOMENT, Time-MoE, TTM/TinyTimeMixers, Lag-Llama, Toto, UniTS, Timer

"Ten models, three good ideas, and a great deal of marketing. My job is to tell which is which before I commit a GPU to it."

A Discriminating AI Agent

This section assumes you have read Section 19.1 on what qualifies a model as "foundational" and Section 19.2 on patching versus value tokenization; those two ideas are the axes we lean on hardest here. The transformer and state-space backbones underneath these models come from Chapter 15 and Chapter 16, and the probabilistic-output vocabulary (quantiles, calibration) comes from Chapter 18. If any of those are unfamiliar, skim them first.

The five axes that actually separate the families

Before the names, fix the coordinate system. Every model in the title differs along at most five choices, and once you know a model's coordinates you can predict its strengths.

• Tokenization. Patch-and-project (a window of \(P\) raw values becomes one embedding) versus value quantization (each scaled value is mapped to a discrete token from a fixed vocabulary) versus lag features (past values at fixed lags become the input vector). This is the single biggest divider, developed fully in Section 19.2.
• Backbone. Decoder-only autoregressive, encoder-only masked reconstruction, or encoder-decoder. Decoder-only rolls out long horizons naturally; encoder-only shines at embeddings, imputation, and classification.
• Output head. A point value, a set of quantiles, a parametric distribution (Student-t, mixture), or a categorical distribution you sample from to build trajectories. This determines whether you get honest uncertainty for free.
• Channel handling. Univariate (each channel forecast independently) versus any-variate (attention across an arbitrary number of correlated channels). Multi-sensor rigs need the latter.
• Capacity and sparsity. Dense parameters versus mixture-of-experts (MoE), and raw size from roughly one million to several billion. This sets your latency and edge feasibility.

Decoder-only forecasters: TimesFM, Time-MoE, Timer, Toto, Lag-Llama

TimesFM (Google, 200M and 500M) is the reference decoder-only patched forecaster: input patches of length 32, output patches that can be longer than input patches so a single forward pass covers a long horizon, trained on Google Trends, Wikipedia pageviews, and synthetic series. It began as a point forecaster and later added quantile heads. It is the model to reach for when you want strong univariate zero-shot forecasting with a well-maintained checkpoint.

Time-MoE pushes the same decoder-only recipe to billion-parameter scale but keeps inference cheap by activating only a few experts per token; it is pretrained on the Time-300B corpus. Timer (Tsinghua) is a GPT-style generative pretrainer that casts forecasting, imputation, and anomaly detection into one "single-series sequence" format so one autoregressive model serves several tasks. Toto (Datadog) is a decoder-only model tuned for the observability world, pretrained on an enormous internal telemetry corpus and released alongside the BOOM benchmark of real infrastructure metrics; it is the natural pick when your "sensors" are server and network counters. Lag-Llama is the important early probabilistic univariate model: it feeds lagged values plus date features into a LLaMA-style decoder and emits a Student-t distribution, giving calibrated predictive intervals rather than a bare point.

Value-tokenized and any-variate families: Chronos, Chronos-Bolt, Moirai, Moirai-MoE

Chronos (Amazon) took the boldest shortcut: scale a series, quantize each value into one of a few thousand bins, and train an off-the-shelf T5 language model to predict the next token. Forecasting becomes literal language modeling, and uncertainty comes from sampling many token trajectories. It is elegant and strong, but sampling is slow. Chronos-Bolt fixes that by switching to patch-based direct multi-step decoding, dropping autoregressive sampling; it runs on the order of hundreds of times faster and often more accurately, which is why Bolt, not the original, is what you should deploy.

Moirai (Salesforce) is the flagship any-variate masked-encoder model: a flattened multi-channel input, "any-variate attention" that generalizes across an arbitrary number of correlated channels, multiple patch-size projections for different sampling rates, and a mixture-distribution output. It is pretrained on LOTSA, the large open time-series archive discussed in Section 19.6. Moirai-MoE replaces the hand-designed multi-patch projections with token-level sparse experts, letting the model route different frequency regimes to different experts and matching or beating the dense version with fewer active parameters. When your rig streams many correlated channels (a six-axis IMU, a multi-thermocouple furnace), an any-variate model is structurally the right choice.

General-purpose and tiny families: MOMENT, UniTS, TTM/TinyTimeMixers

MOMENT (CMU) is the encoder-only, masked-reconstruction generalist: pretrained on the Time-Series Pile, it produces embeddings you attach lightweight heads to for forecasting, classification, imputation, or anomaly detection. It is less a forecaster and more a feature extractor, the subject of Section 19.5. UniTS shares that multi-task spirit but bakes task tokens into a single unified network so one set of weights serves forecasting and classification without swapping heads.

TTM / TinyTimeMixers (IBM, granite-tsfm) is the outlier that matters most for edge deployment. Instead of a transformer it uses a lightweight TSMixer (MLP-Mixer) backbone at roughly one to five million parameters, small enough to run zero-shot forecasting on a CPU in milliseconds. It concedes some accuracy on the hardest series but wins decisively on cost, and it is the honest counter-example to the assumption that a foundation model must be huge.

Loading two families zero-shot

The point of a foundation model is that "training" collapses to a download. The snippet below loads a fast value-tokenized forecaster (Chronos-Bolt) and a tiny mixer (TTM) and forecasts the same context, so you can compare a heavyweight and a featherweight on your own sensor in a dozen lines.

import numpy as np, torch
from chronos import BaseChronosPipeline           # pip install chronos-forecasting
from tsfm_public import get_model                 # pip install granite-tsfm (IBM TTM)

context = torch.tensor(np.load("furnace_zone3.npy"), dtype=torch.float32)  # past values
H = 48                                            # 48-step (30 min) horizon

# Chronos-Bolt: patch-based direct decoding, quantile output, no sampling
bolt = BaseChronosPipeline.from_pretrained("amazon/chronos-bolt-small",
                                           device_map="cpu", torch_dtype=torch.float32)
q, mean = bolt.predict_quantiles(context=context, prediction_length=H,
                                 quantile_levels=[0.1, 0.5, 0.9])
lo, med, hi = q[0, :, 0], q[0, :, 1], q[0, :, 2]  # 10/50/90 percentile bands

# TinyTimeMixer: ~1M params, CPU-friendly zero-shot
ttm = get_model("ibm-granite/granite-timeseries-ttm-r2",
                context_length=512, prediction_length=H)
ttm.eval()
with torch.no_grad():
    ttm_pred = ttm(context.reshape(1, -1, 1)).prediction_outputs.squeeze()

print("Chronos-Bolt median[:3]:", med[:3].tolist())
print("TTM point forecast[:3] :", ttm_pred[:3].tolist())

What's Next

In Section 19.4, we put these checkpoints to work: how the same pretrained weights perform zero-shot and few-shot across forecasting, classification, imputation, and anomaly detection, why some tasks transfer far better than others, and how to run a fair, leakage-safe comparison against a task-specific baseline before you trust any of the numbers a model card advertises.