Amazon.com, Inc. (AMZN)
Amazon.com, Inc. is an American multinational technology company focusing on e-commerce, cloud computing, online advertising, digital streaming, and artificial intelligence.
Stock Price Trends
Stock price trends estimated using linear regression.
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 88.27% per annum.
- AMZN price at the close of December 8, 2023 was $147.42 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 11.20% per annum.
- AMZN price at the close of December 8, 2023 was higher than the top border of the secondary price channel by $0.42 (0.28%).
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of AMZN price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: November 18, 2022
End date: September 20, 2023
a = 1.9349
b = 0.0017
s = 0.0528
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 88.27%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0528) – 1
= 23.51%
November 18, 2022 calculations
Top border of price channel:
Exp(Y994)
= Exp(a + b × X994 + 2 × s)
= Exp(a + b × 1,439 + 2 × s)
= Exp(1.9349 + 0.0017 × 1,439 + 2 × 0.0528)
= Exp(4.5348)
= $93.21
Bottom border of price channel:
Exp(Y994)
= Exp(a + b × X994 – 2 × s)
= Exp(a + b × 1,439 – 2 × s)
= Exp(1.9349 + 0.0017 × 1,439 – 2 × 0.0528)
= Exp(4.3237)
= $75.46
September 20, 2023 calculations
Top border of price channel:
Exp(Y1,202)
= Exp(a + b × X1,202 + 2 × s)
= Exp(a + b × 1,745 + 2 × s)
= Exp(1.9349 + 0.0017 × 1,745 + 2 × 0.0528)
= Exp(5.0653)
= $158.42
Bottom border of price channel:
Exp(Y1,202)
= Exp(a + b × X1,202 – 2 × s)
= Exp(a + b × 1,745 – 2 × s)
= Exp(1.9349 + 0.0017 × 1,745 – 2 × 0.0528)
= Exp(4.8541)
= $128.26
Secondary Trend
Start date: May 26, 2023
End date: November 6, 2023
a = 4.3786
b = 0.0003
s = 0.0407
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 11.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0407) – 1
= 17.67%
May 26, 2023 calculations
Top border of price channel:
Exp(Y1,123)
= Exp(a + b × X1,123 + 2 × s)
= Exp(a + b × 1,628 + 2 × s)
= Exp(4.3786 + 0.0003 × 1,628 + 2 × 0.0407)
= Exp(4.9334)
= $138.86
Bottom border of price channel:
Exp(Y1,123)
= Exp(a + b × X1,123 – 2 × s)
= Exp(a + b × 1,628 – 2 × s)
= Exp(4.3786 + 0.0003 × 1,628 – 2 × 0.0407)
= Exp(4.7707)
= $118.01
November 6, 2023 calculations
Top border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 + 2 × s)
= Exp(a + b × 1,792 + 2 × s)
= Exp(4.3786 + 0.0003 × 1,792 + 2 × 0.0407)
= Exp(4.9811)
= $145.64
Bottom border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 – 2 × s)
= Exp(a + b × 1,792 – 2 × s)
= Exp(4.3786 + 0.0003 × 1,792 – 2 × 0.0407)
= Exp(4.8184)
= $123.77