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 110.16% per annum.
- META price at the close of February 20, 2025 was $694.84 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 41.75% per annum.
- META price at the close of February 20, 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 META 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: September 13, 2022
End date: February 20, 2025
a = 2.9684
b = 0.0020
s = 0.1502
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0020) – 1
= 110.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1502) – 1
= 82.32%
September 13, 2022 calculations
Top border of price channel:
Exp(Y645)
= Exp(a + b × X645 + 2 × s)
= Exp(a + b × 935 + 2 × s)
= Exp(2.9684 + 0.0020 × 935 + 2 × 0.1502)
= Exp(5.1713)
= $176.14
Bottom border of price channel:
Exp(Y645)
= Exp(a + b × X645 – 2 × s)
= Exp(a + b × 935 – 2 × s)
= Exp(2.9684 + 0.0020 × 935 – 2 × 0.1502)
= Exp(4.5707)
= $96.61
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.9684 + 0.0020 × 1,826 + 2 × 0.1502)
= Exp(6.9843)
= $1,079.52
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.9684 + 0.0020 × 1,826 – 2 × 0.1502)
= Exp(6.3837)
= $592.09
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 110.16% per annum.
- META price at the close of February 20, 2025 was $694.84 and was inside the primary price channel.
Secondary Trend
Start date: February 2, 2024
End date: February 20, 2025
a = 4.7216
b = 0.0010
s = 0.0576
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 41.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0576) – 1
= 25.91%
February 2, 2024 calculations
Top border of price channel:
Exp(Y994)
= Exp(a + b × X994 + 2 × s)
= Exp(a + b × 1,442 + 2 × s)
= Exp(4.7216 + 0.0010 × 1,442 + 2 × 0.0576)
= Exp(6.2151)
= $500.26
Bottom border of price channel:
Exp(Y994)
= Exp(a + b × X994 – 2 × s)
= Exp(a + b × 1,442 – 2 × s)
= Exp(4.7216 + 0.0010 × 1,442 – 2 × 0.0576)
= Exp(5.9847)
= $397.30
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.7216 + 0.0010 × 1,826 + 2 × 0.0576)
= Exp(6.5822)
= $722.11
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.7216 + 0.0010 × 1,826 – 2 × 0.0576)
= Exp(6.3517)
= $573.49
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 41.75% per annum.
- META price at the close of February 20, 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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