Moving avg using OVER RANGE BETWEEN days

I want to find the average of item price bought within the last 365 days. Items are not guaranteed to be bought every day, so I can't fix the number of rows to look back at. So I am trying to use RANGE instead of ROWS, specifying that I look back 365 days from current row's date.

Sample data:

• Group by Store and Item
• I want to find the avg of prices bought within the last 12 months

I have tried:

SELECT  
    store, item, date, price,
    SUM(price) OVER (PARTITION BY store, item
                     ORDER BY date ASC
                     RANGE BETWEEN 365 DAY PRECEDING AND CURRENT ROW) AS avg_price
FROM table

Error I get is:

Msg 102, Level 15, State 1, Line 102
Incorrect syntax near 'DAY'

I have tried these variations to address the error but can't get past it:

1. RANGE BETWEEN '365' DAY PRECEDING AND CURRENT ROW
2. RANGE BETWEEN INTERVAL 365 DAY PRECEDING AND CURRENT ROW
3. RANGE BETWEEN 365 PRECEDING AND CURRENT ROW

#3 produces the error

Msg 4194, Level 16, State 1, Line 98
RANGE is only supported with UNBOUNDED and CURRENT ROW window frame delimiters.

Is this a syntax error? I am using Microsoft SQL Server Management Studio.

A good old self-join should work (I converted your dates into ISO format):

with cte as (
    select *
    
    from (
        VALUES  (N'Store 1', N'Item 1', N'2022-01-02', 1.00, 1.00)
        ,   (N'Store 1', N'Item 1', N'2022-06-01', 1.75, 1.375)
        ,   (N'Store 1', N'Item 1', N'2022-11-01', 2.10, 1.617)
        ,   (N'Store 1', N'Item 1', N'2023-01-05', 3.00, 2.283)
        ,   (N'Store 2', N'Item 1', N'2022-03-02', 1.55, 1.55)
        ,   (N'Store 2', N'Item 1', N'2022-05-05', 2.80, 2.175)
    ) t (Store,Item,[Date bought],Price,[Avg price across last 365 days])
    )
select  AVG(c2.price), c.Store, c.Item, c.[Date bought]
from CTE c
LEFT JOIN CTE c2
    On  c2.Store = c.Store
    AND c2.Item = c.Item
    AND c2.[Date bought]  between DATEADD(YEAR, -1,CAST(c.[Date bought] AS DATETIME)) AND c.[Date bought]
GROUP BY c.Store, c.Item, c.[Date bought]