Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 52.14% per annum.
- AMZN price at the close of May 16, 2025 was $205.59 and was lower than the bottom border of the primary price channel by $23.23 (10.15%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.75% per annum.
- AMZN price at the close of May 16, 2025 was inside the secondary price channel.
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: October 28, 2022
End date: February 21, 2025
a = 3.4758
b = 0.0011
s = 0.0700
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 52.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0700) – 1
= 32.31%
October 28, 2022 calculations
Top border of price channel:
Exp(Y618)
= Exp(a + b × X618 + 2 × s)
= Exp(a + b × 893 + 2 × s)
= Exp(3.4758 + 0.0011 × 893 + 2 × 0.0700)
= Exp(4.6425)
= $103.80
Bottom border of price channel:
Exp(Y618)
= Exp(a + b × X618 – 2 × s)
= Exp(a + b × 893 – 2 × s)
= Exp(3.4758 + 0.0011 × 893 – 2 × 0.0700)
= Exp(4.3625)
= $78.46
February 21, 2025 calculations
Top border of price channel:
Exp(Y1,197)
= Exp(a + b × X1,197 + 2 × s)
= Exp(a + b × 1,740 + 2 × s)
= Exp(3.4758 + 0.0011 × 1,740 + 2 × 0.0700)
= Exp(5.6163)
= $274.88
Bottom border of price channel:
Exp(Y1,197)
= Exp(a + b × X1,197 – 2 × s)
= Exp(a + b × 1,740 – 2 × s)
= Exp(3.4758 + 0.0011 × 1,740 – 2 × 0.0700)
= Exp(5.3364)
= $207.75
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 52.14% per annum.
- AMZN price at the close of May 16, 2025 was $205.59 and was lower than the bottom border of the primary price channel by $23.23 (10.15%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 2, 2024
End date: May 16, 2025
a = 4.6210
b = 0.0004
s = 0.0772
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 15.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0772) – 1
= 36.19%
February 2, 2024 calculations
Top border of price channel:
Exp(Y934)
= Exp(a + b × X934 + 2 × s)
= Exp(a + b × 1,355 + 2 × s)
= Exp(4.6210 + 0.0004 × 1,355 + 2 × 0.0772)
= Exp(5.3184)
= $204.05
Bottom border of price channel:
Exp(Y934)
= Exp(a + b × X934 – 2 × s)
= Exp(a + b × 1,355 – 2 × s)
= Exp(4.6210 + 0.0004 × 1,355 – 2 × 0.0772)
= Exp(5.0095)
= $149.83
May 16, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.6210 + 0.0004 × 1,824 + 2 × 0.0772)
= Exp(5.5063)
= $246.23
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.6210 + 0.0004 × 1,824 – 2 × 0.0772)
= Exp(5.1974)
= $180.80
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.75% per annum.
- AMZN price at the close of May 16, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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